Essential Mathematicsfor GCSE Foundation tier

Homework book

Michael White

Elmwood Press

First published 2006 byElmwood Press80 Attimore RoadWelwyn Garden CityHerts AL8 6LPTel. 01707 333232

Copyright notice

All rights reserved. No part of this publication may be reproduced in any form orby any means (including photocopying or storing it in any medium by electronicmeans and whether or not transiently or incidentally to some other use of thispublication) without the written permission of the copyright owner, except inaccordance with the provisions of the Copyright, Designs and Patents Act 1988 orunder the terms of a licence issued by the Copyright Licensing Agency,90 Tottenham Court Road, London W1P 0LP. Applications for the copyrightowner’s written permission should be addressed to the publisher.

The moral rights of the author have been asserted.Database right Elmwood press (maker)

ISBN 1 902 214 65X

� Michael White

Typeset and illustrated by TnQ Books and Journals Pvt. Ltd., Chennai, India.

Printed by WS Bookwell, Finland.

Contents

Unit 1

Number 1Place value 1Rounding off 1Adding and subtracting whole

numbers 2Multiplying whole numbers 3Dividing whole numbers 4Negative numbers 5Order of operations 7

Unit 2

Number 2Square and square root 7Cube and cube root 8Powers 8Factors and prime numbers 9Multiples and LCM 10Highest common factor 10Prime factor decomposition 10Equivalent fractions 11Ordering fractions 12Converting between fractions

and decimals 13Ordering decimals 13

Unit 3

Shape 1Types of angle 14Angles on a straight line, angles

at a point 16Vertically opposite angles,

angles in a triangle 16Isosceles and equilateral

triangles 17

Parallel lines 17Symmetry – reflection and

rotational 18Planes of symmetry 19Common quadrilaterals 20Angles in polygons 20

Unit 4

Algebra 1Basic algebra 23Substituting numbers for letters 24Collecting and simplifying terms 26Multiplying brackets 29Common factors 30

Unit 5

Number 3Basic fractions 31Fraction of a number 32Improper fractions and mixed

fractions 32Adding and subtracting fractions 33Multiplying fractions 34Dividing fractions 35

Unit 6

Number 4Converting fractions and

percentages 35Percentage of a number 36Percentage increase and

decrease 39Converting percentages and

decimals 40

Percentage changes 41Compound interest 42Ratio 42Direct proportion 43Sharing in a ratio 44

Unit 8

Shape 2Congruent shapes 45Coordinates 47Translating shapes 49Reflecting shapes 50Rotating shapes 52Enlarging shapes 54

Unit 9

Number 5Adding and subtracting decimals 57Multiplying decimals 59Dividing decimals by whole

numbers 60Dividing by decimals 60Rounding off to nearest 10,

100, 1000 61Decimal places 62Estimating 63Using a calculator 63Significant figures 65Checking answers 66

Unit 10

Algebra 2Straight line graphs 66Curved graphs 68Simultaneous equations,

graphical solution 70Gradient 70Reading graphs 72Travel graphs 73

Unit 11

Data 1The probability scale 74Relative frequency 75Finding probabilities 76Listing possible outcomes 77Mutually exclusive events 78

Unit 12

Algebra 3Sequences 79Sequence rules 80Solving equations 83Solving equations with brackets

and with unknown on bothsides 86

Setting up equations 87Trial and improvement 89

Unit 13

Data 2Averages and range 90Charts and graphs 92Stem and leaf diagrams 94Pie charts 95Two-way tables 96

Unit 15

Shapes 3Perimeter 97Areas of triangles and

rectangles 99Areas of trapeziums and

parallelograms 100Circumference of a circle 101Area of a circle 103Surface areas and volumes

of cuboids 104

Converting units of area andvolume 105

Volume of prisms, cylinders 105Similar triangles 107Dimensions of a formula 108

Unit 16

Data 3Scatter diagrams, correlation 109Line of best fit 110Median and mode from

tables 110Mean from frequency tables 112Comparing sets of data 113

Unit 17

Shape 4Scale reading 115Metric units 117Time problems 118Imperial units 118Converting metric and

imperial units 119Upper and lower bounds 120Speed, density and other

compound measures 121

Unit 18

Algebra 4Changing the subject of

a formula 123Inequalities 124Indices 125Standard form 126

Unit 19

Shape 5Measuring lengths and angles 128Constructing triangles 130Construction with compasses 131Scale drawing 133Map scales 134Locus 135

Unit 20

Shape 6Nets 1383-D objects, isometric drawing 141Plans and elevations 141Bearings 143Pythagoras’ theorem 145Problems involving coordinates 147Coordinates in 3 dimensions 148

NUMBER 1 1

TASK 1.1

M�1 What is the value of the underlined digit in each number below:

a 326 b 518 c 6173 d 4953 e 204

�2 5 3 4

a Using all the 3 cards above, what is the smallest number you can

make?

b Using all the 3 cards above, what is the largest number you can

make?

�3 Jamie bought a new sofa for £1350. Write down the value of the

5 digit.

�4 Annie sold her car for £5750. Write down the value of the

7 digit.

E�1 The 7 in the number 24·73 means 710

. What is the value of the

underlined digit in each number below:

a 0·69 b 0·437 c 0·328 d 0·58

e 9·714 f 3·628 g 23·748 h 46·207

�2 Which number is the smaller: 0·03 or 0·3

�3 Which number is the larger: 0·6 or 0·09

�4 Which number is the smallest: 0·7 0·008 0·06

TASK 1.2

M�1 Round to the nearest 10.

a 38 b 43 c 84 d 75 e 328

�2 Round to the nearest 100.

a 340 b 764 c 350 d 1240 e 1550

1

�3 Round to the nearest 1000.

a 3700 b 5550 c 7143 d 4238 e 6500

�4 Carl has £13·64. Round this to the nearest pound.

�5 Maria weighs 54·37 kg. Round this to the nearest kilogram.

�6 Round to the nearest whole number.

a 6·8 b 4·5 c 7·6 d 13·2 e 18·5

E�1 Work out these answers with a calculator and then round off the answers to the

nearest whole number.

a 7·1 · 3·89 b 6·31 · 4·75 c 5·08 · 3·17 d 693 4 19

e 512 4 4·67 f 71·4 4 5·26 g 5·61 4 13 h 6·82 · 1·78

�2 One evening around 300 people visit a nightclub. This number is

rounded off to the nearest 100. Which of the numbers below could be

the exact number of people at the nightclub?

260 349 249 359 302 393 287 238

�3 Round off 16 456 to

a the nearest 10 b the nearest 100 c the nearest 1000.

TASK 1.3

M

Copy and complete.�1 4 7 �2 5 6 4 �3 3 1 2 7 �4 6 4 �5 8 3

+ 6 4 + 2 3 9 + 4 3 8 6 2 3 7 2 4 8

�6 4 8 1 �7 5 9 8 �8 4 6 2 8 �9 6 2 1 7 �10 3 8 7 4 2

2 2 6 4 2 3 1 9 2 1 3 8 6 2 4 4 0 6 + 1 2 6 3 8

�11 387 + 519 �12 462 2 181 �13 1374 2 648

E�1 Hannah has saved £415. She wants to buy a music centre costing £694.

How much more money must she save?

2

�2 The following people collect money for a Cancer charity.

Ellie £138 Dan £193 Shalina £68

Katie £89 Callum £47 Jack £204

How much money have they collected in total?

�3 Find the difference between 592 and 176.

�4 Marcus is taking part in a 1290 mile car rally. He has completed

863 miles. How many more miles must he cover?

Copy and complete Questions�5 to�10 by writing the missing number

in the box.�5 360 + = 589 �6 270 + = 440 �7 348 2 = 230�8 712 2 = 508 �9 1365 2 = 980 �10 2 286 = 461

TASK 1.4

M�1 Work out

a 72 · 100 b 4160 · 10 c 586 000 4 10

d 673 000 4 100 e 570 · 100 f 6720 · 1000

�2 Copy and complete

a 4 100 = 47 b · 100 = 3800 c · 10 = 4800

d 160 · = 16 000 e 36 000 4 = 3600 f · 100 = 72 000

g ! · 100 ! 21 500 ! 4 10 ! ! · 100 !

�3 A group of 100 people won £8 000 000 on the National Lottery. How

much money did each person win if they each received an equal share?

E�1 Work out

a 20 · 60 b 900 · 30 c 1500 4 30

d 6400 4 800 e 36 000 4 90 f 400 · 700

�2 Copy and complete

a · 40 = 3200 b · 200 = 8000 c · 90 = 540

d 4 50 = 60 e 72 000 4 = 90 f 4 300 = 70

�3 30 houses each costing £90 000 are built on a housing estate. What is

the total cost of all 30 houses?

3

TASK 1.5

M

Work out�1 4 2 �2 6 3 �3 3 7 �4 49 · 3 �5 6 · 84

· 4 · 5 · 8

�6 3 0 4 �7 5 2 6 �8 4 6 3 �9 738 · 6 �10 9 · 284

· 3 · 4 · 8

�11 629 students at a school each pay £6 to go on a school trip. How much

money do they pay in total?

E

Work out without a calculator.�1 32 · 14 �2 17 · 24 �3 42 · 23 �4 64 · 34�5 213 · 15 �6 421 · 36 �7 839 · 28 �8 627 · 56

�9 One evening a restaurant sells 37 set dinners at £16 each. How much

money does the restaurant receive in total for these 37 meals?

�10 At the World Cup there were 24 teams. If each team had a squad of

26 players, how many players were there in total?

TASK 1.6

M

Work out�1 48 4 6 �2 28 4 4 �3 36 4 9 �4 72 4 8 �5 56 4 7�6 3Þ69 �7 4Þ136 �8 6Þ438 �9 8Þ296 �10 7Þ1512�11 384 4 8 �12 354 4 6 �13 375 4 5 �14 2457 4 7 �15 2898 4 6

E

Work out each answer, giving the remainder.�1 4Þ583 �2 5Þ712 �3 8Þ316 �4 6Þ2715 �5 9Þ4814�6 828 4 7 �7 486 4 5 �8 377 4 8 �9 4386 4 7 �10 7245 4 4

�11 43 children are playing in a 5-a-side tournament. How many

complete teams of 5 players can be made?

4

�12 A calculator costs £7. How many calculators can a school buy for £225?

�13 A wine box at a supermarket can hold 6 bottles. How many boxes

are needed to hold 112 bottles?

TASK 1.7

M

Work out�1 448 4 16 �2 612 4 17 �3 575 4 23 �4 576 4 36�5 986 4 29 �6 774 4 18 �7 988 4 26 �8 722 4 38

E�1 A book of stamps contains 36 stamps. How many books must I buy if

I need 850 stamps?

�2 1500 sweets are shared equally into 46 packets. How many

sweets will be in each packet and how many sweets will be

left over?

�3 Which answer is the odd one out?

891 4 33 406 4 14 648 4 24

A B C�4 One coach may carry 47 people. How many coaches are needed to

transport 560 football fans to an away match?

�5 37 screws are used to make a flat pack desk. If a factory has

623 screws remaining, how may flat packs could the factory supply?

TASK 1.8

M�1 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 °C

P Q R S T

The difference in temperature between Q and R is 2 �C. Give the

difference in temperature between:

a R and S b Q and S c R and T d P and T

5

�2 The temperature in Liverpool is 23 �C and the temperature in

Plymouth is 2 �C. How much warmer is Plymouth than

Liverpool?

�3 The temperature in Hull is 21 �C. The temperature rises by 8 �C.

What is the new temperature in Hull?

�4 Work out

a 2 2 7 b 23 2 2 c 24 + 1 d 29 2 2 e 26 + 5

�5 What is the difference between the two smallest numbers

below?

4 �6 �3 1 5 �4

E�1 Work out

a 5 2 23 b 7 + 24 c 22 2 3 d 25 2 1 e 26 + 2

f 27 2 21 g 24 2 24 h 23 + 26 i 22 + 26 j 26 2 26

�2 Copy and complete the boxes below:

a 3 2 = 25 b 2 1 = 24 c 29 + = 23

d 2 24 = 22 e 24 2 = 210 f + 27 = 25

�3 Work out

a 24 + 2 2 3 b 21 2 6 + 4 c 29 + 6 2 21

d 22 + 23 + 24 e 28 2 26 + 23 f 23 2 9 2 24 2 2

TASK 1.9

M�1 Work out

a 6 · 24 b 23 · 8

c 22 · 24 d 210 4 2

e 228 4 24 f 230 4 25

g 27 · 26 h 29 · 8

i 48 4 26 j 26 · 9

k 235 4 7 l 230 4 6

m 281 4 29 n 27 · 28

�2 Copy and complete the multiplication square

below:

× −4

−12

−24 −12

−45

3

24

40

−8

6

E

Each empty square contains either a number or an operation (+, 2, ·, 4).

Copy each square and fill in the missing details. The arrows are equals signs.�1 16 ÷

÷

×

×

−4

−8 + 5

�2 12×

×

−3

−7 −6−

−21

�3 −15 +

÷ ×

−5

−3

−10 133

TASK 1.10

M�1 Work out

a 6 + 4 · 2 b 5 + 2 · 3 c (3 + 2) · 6 d 32 4 4 + 6

e 4 · 7 + 3 f 30 4 (4 + 1) g 6 · (9 2 3) h 5 + 6 · 3 + 2

i (5 + 4) 4 3 + 7 j (5 + 7) 4 (6 2 2) k 28 2 3 · 6 l 4 + 6 · 2 4 2

m (8 2 3) · (4 + 5) n (8 + 3 + 9) 4 5 o 36 4 (2 + 7) p (4 + 16) 4 (8 2 3)

E�1 Work out

a 28 + 12 · 3 b (28 + 12) · 3 c 63 2 14 · 3 d 21 + 20 4 2

e 56 4 (3 + 5) f (13 + 17) · (62 2 12) g 4 + 16 · 5 h 50 2 100 4 4

i 72 4 8 2 32 4 4 j 28 + 48 4 12 k 31 2 9 · 3 + 16 l 39 + 63 4 7

�2 Copy each Question and write brackets so that each calculation gives

the correct answer.

a 7 · 4 + 2 = 42 b 6 + 9 4 3 = 5 c 6 + 3 · 4 = 36 d 4 + 3 · 8 2 6 = 14

e 12 + 6 4 9 = 2 f 15 2 6 · 3 + 6 = 81 g 8 · 4 2 2 = 16 h 72 4 2 + 6 = 9

NUMBER 2 2

TASK 2.1

M�1 32 = 3 · 3 = 9. Find the value of

a 52 b 72 c 62 d 12 e 302

7

�2 ffiffiffiffiffi49p

= 7 because 7 · 7 = 49. Find the value of

affiffiffiffiffi16p

bffiffiffiffiffi36p

cffiffiffiffiffiffiffiffi100p

dffiffiffiffiffi64p

effiffiffi1p

�3 What is the length of one side of this square?

area = 25 cm2

�4 Write down the square root of 400.

�5 Find the value of

a 32 + 42 b 92 2 42 c (8 2 2)2

d 102 + 62 effiffiffiffiffi81p

2ffiffiffi4p

fffiffiffiffiffi16p

+ffiffiffiffiffi25p

gffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(28 + 21)p

hffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(63 2 59)p

iffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(62 + 82)

p

E�1 73 = 7 · 7 · 7 = 49 · 7 = 343. Find the value of

a 23 b 43 c 13 d 53 e 103

�2 How many small cubes are needed

to make this giant cube?

�3 ffiffiffiffiffi643p

= 4 because 4 · 4 · 4 = 64. Find the value of

affiffiffi83p

bffiffiffi13p

cffiffiffiffiffiffiffiffi1253p

dffiffiffiffiffi273p

�4 Write down the cube root of 1000.

�5 Find the value of

affiffiffiffiffiffiffiffiffiffiffiffiffiffi(5 + 3)3p

bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(62 + 42 + 12)3

pc (32 2 22)3

TASK 2.2

M only�1 4 · 4 · 4 · 4 · 4 means ‘4 to the power 5’ which is written as 45

(index form). Write the following in index form.

a 3 · 3 · 3 · 3 b 2 · 2 · 2 · 2 · 2 · 2

c 7 · 7 · 7 · 7 · 7 d 10 · 10 · 10

8

�2 35 means 3 · 3 · 3 · 3 · 3. Copy and complete the following:

a 94 means ...................... b 54 means ......................

c 66 means ...................... d 27 means ......................

�3 Which is smaller? 32 or 23

�4 Which is smaller? 52 or 25

�5 Find the value of

a 2 · 32 b 33 · 4 c 53 · 22

Use a calculator for the Questions below:�6 Find the value of

a 54 b 36 c 4 · 4 · 4 · 4 · 4 d 105

e 75 f 212 g 6 to the power 7 h 3 · 3 · 3 · 3 · 3

i 8 · 8 · 8 · 8 j 38 k 47 l 8 to the power 6

�7 Write down the next two numbers in this sequence:

3, 9, 27, 81, 243, ......, ......

�8 How many numbers are in the sequence below up to and including 512?

2, 4, 8, 16, ......................, 512

TASK 2.3

M

Write down all the factors of the following numbers:�1 20 (6 factors) �2 12 (6 factors) �3 29 (2 factors)�4 18 �5 32 �6 50

�7 Which of these numbers are:

2 11

13 5 69 14

a even numbers? b odd numbers?

c prime numbers? d factors of 24?

�8 Write down all the even factors of 24.

�9 Write down all the factors of 35 which are prime.

�10 Which numbers between 30 and 40 have 4 as a factor?

E�1 Write down the first 5 multiples of:

a 3 b 6 c 9 d 8 e 12

9

�2 Which of these numbers are:

2118

4263

54

2826

a multiples of 6

b multiples of 7

c not multiples of 2

�3 Copy and complete the first five multiples of 6 and 10.

6: 6 12

10: 10

Write down the Lowest Common Multiple of 6 and 10.

�4 Find the Lowest Common Multiple of each of these pairs of numbers.

a 5 and 8 b 8 and 12 c 10 and 60

�5 Amy and Josh are racing each other. Amy takes 5 minutes to

complete one lap. Josh takes 7 minutes to complete one lap.

After how many minutes will Amy and Josh pass the starting

point at exactly the same time?

TASK 2.4

M�1 a List all the factors of 18.

b List all the factors of 30.

c Write down the Highest Common Factor of 18 and 30.

�2 a List all the factors of 30.

b List all the factors of 45.

c Write down the Highest Common Factor of 30 and 45.

�3 Find the Highest Common Factor of:

a 20 and 50 b 25 and 60

c 36 and 60 d 16, 32 and 40

E�1 Work out

a 3 · 3 · 5 b 22 · 7 c 22 · 32

�2 For each Question below, find the number which belongs in the

empty box:

a 60 = 22 · 3 · b 40 = 23 · c 126 = 2 · 32 ·

10

�3 Using any method, write the following numbers as products of

prime factors:

a 75 b 44 c 80 d 594

�4 1617 = 3 · 7 · 7 · 11 and 273 = 3 · 7 · 13

Find the Highest Common Factor of 273 and 1617.

�5 Write 315 and 495 as products of prime factors. Use this to find

the Highest Common Factor of 315 and 495.

�6 Write 396 and 420 as products of prime factors. Use this to find

the Highest Common Factor of 396 and 420.

TASK 2.5

M�1 Which shapes have an equivalent fraction shaded?

A B C

�2 Copy this rectangle.

Shade a fraction equivalent to 3

5.

�3 Copy and complete these equivalent fractions by filling in the box.

a 3

4=

20b 1

3=

12c 5

8=

10 d 2

9=

36

e 3

8=

15 f 7

20=

35 g 4

5=

30h 5

9=

45

E�1 Cancel each fraction below to its lowest terms.

a 18

20b 12

30c 6

15d 24

32e 6

18

f 25

100g 21

28h 32

48i 63

81j 88

121

11

�2 Which of the fractions below are the same as 7

8?

a 21

24b 16

18c 14

24d 35

40e 21

27f 56

64

�3 Find the fractions in the table which are equivalent to 4

9.

Rearrange the chosen letters to show a salad vegetable.

32

72

40

90

12

20

45

81

28

63

20

45

28

56

12

27

16

45

24

54

D H B U S A M R Y I

TASK 2.6

M only�1 Copy and use the diagrams to

explain why 2

3is larger than 7

12.

�2 a 1

2=

16b Which is larger, 1

2or 9

16?

�3 Write down the smaller fraction:

a 5

8or 3

4b 9

10or 26

30c 6

7or 7

8�4 Place in order, largest first:

a 7

20,1

4,

3

10b 11

16,5

8,19

32

c 13

18,2

3,5

9d 1

8,

5

48,1

6�5 a 3

8=

16b 1

2=

16c Does 7

16lie between 3

8

and 1

2?

�6 a 1

4=

40b 3

10=

40c Write down a fraction which

lies between 1

4and 3

10.

12

�7 a 5

7=

35b 4

5=

35c Write down a fraction which lies

between 5

7and 4

5.

�8 For each pair of fractions below, write down a fraction which lies

between them:

a 4

15and 1

3b 5

6and 11

12c 7

10and 8

10

TASK 2.7

M�1 Is 0·027 the same as 27

1000?

�2 Is 0·8 the same as 4

5?

�3 Is 0·45 the same as 7

20?

�4 Change the following decimals to fractions in their most

simple form.

a 0·03 b 0·82 c 0·4 d 0·052 e 0·15

�5 Copy the Questions below and fill in the boxes.

a 11

20=

100= 0· b 7

200=

1000= 0·

�6 Convert the fractions below to decimals.

a 3

20b 19

25c 103

200d 3

8e 13

25

�7 Change the fractions below to decimals by dividing the numerator by

the denominator.

a 5

9b 1

11c 5

12

E�1 Which is larger?

a 0·06 or 0·5 b 0·038 or 0·04 c 0·74 or 0·742

�2 0·03 > 0·026 Is this true or false?

�3 0·6 < 0·546 Is this true or false?

13

�4 For each set of numbers below, arrange the numbers in order

of size, smallest first.

a 0·03, 0·3, 0·003

b 0·91, 0·902, 0·92, 0·091

c 0·073, 0·07, 0·75, 0·712

d 0·418, 0·408, 0·48, 0·048

e 7·06, 7·1, 7·102, 7·07, 7·13

�5 In the Questions below, answer True or False.

a 0·08 is more than 0·7 b 0·603 is more than 0·068

c 0·36 is more than 0·308 d 0·4 is less than 0·38

e 0·027 is less than 0·03 f 0·056 is more than 0·07

SHAPE 1 3

TASK 3.1

M�1 For each of these angles say whether they are acute, obtuse or reflex:

a b c d e

f g h i j

�2 Copy and complete the sentences below:

a An acute angle is less than .

b An obtuse angle is more than and less than .

c A reflex angle is more than .

�3 Which of the angles below are obtuse?

187� 45� 120� 193� 243� 138� 31�

�4 Draw a triangle where all the angles are acute.

�5 Can you draw a triangle which has two obtuse angles inside it?

14

�6 How many obtuse angles can you

see in this trapezium?

E�1 The angle BCD is obtuse.

Is angle ADC acute or obtuse?

A

B

C

D

�2 a Is —QRS acute or obtuse?

b Is —SPQ acute or obtuse?Q

S

R

P

�3 Name the marked angles below:

a P

M N

b P Q

R

S

c

H

GF

�4 Estimate the size of each angle stated below:

a

Y Z

X

∠ZYX

b

D

CE

A B

∠AED

c P

Q

S

R∠QPS

15

TASK 3.2

M

Find the angles marked with the letters.

�130°a

�2117°

b�3

80°60°c

�4110°

115°d

�5161°

43°

e

�679° 64°

f�7

56°82°

60°

g

�838°23°

65°h

E�1 a Draw 2 perpendicular lines.

b How large is the angle between the 2 perpendicular lines?

�2 Draw a triangle which has 2 sides which are perpendicular to each

other.

In the Questions below, find the angles marked with the letters.�375°

a�4

76°

38°

b

�558°

73° c �6 de68°

�7f g72°

45°�8

i

h

53°

82°

�9j

k

146°

�10

m

ln

44°

67°

16

TASK 3.3

M

Find the angles marked with the letters.�1a70°

�2 bc

48°

�3 e

fd65°

�4h

g20°

�5 ij �6l

m

k76°

�7 p

o

n 72°

�8q

rs

123°

E

Find the angles marked with the letters.�1a

107°

�239°

b �347°

c

d

�4 110°

fg

e

�5 124°

143°j

h ki

�686° 54°

l

o

nm

�7

115°q

r

p

s �8

86°

30°

v

u t

17

TASK 3.4

M�1 Each of these shapes have a line of symmetry.

Copy them into your book and draw on a dotted line to show the line of symmetry:

�2 Copy the patterns below on squared paper. Shade in as many squares as necessary

to complete the symmetrical patterns. The dotted lines are lines of symmetry.

�3 Sketch these shapes in your book and draw on all the lines of symmetry.

E

For each shape write the order of rotational symmetry (you may use tracing paper).�1 �2 �3 �4

18

�5 �6 �7 �8

�9 Draw your own shape which has an order of rotational symmetry

of 3.

�10 Draw a triangle which has no rotational symmetry.

TASK 3.5

M only�1 How many planes of symmetry does this

triangular prism have?

�2 Draw each shape below and show one plane of symmetry.

a b

c d

19

�3 How many planes of symmetry does

a cube have?

TASK 3.6

M�1 Draw a parallelogram.

�2 How many lines of symmetry does a parallelogram have?

�3 Draw a quadrilateral which has two lines of symmetry only.

�4 Name this shape:

�5 Draw a rhombus in your book.

Draw in the two diagonals.

At the point of intersection of the two diagonals,

write down the angle between the diagonals.

�6 Draw a quadrilateral which has no lines of symmetry.

�7 Copy and complete the two sentences below:

A parallelogram has two pairs of e _ _ _ _ opposite sides and two

pairs of p _ _ _ _ _ _ _ opposite sides. The diagonals cut each

other in h _ _ _.

�8 What is the order of rotational symmetry of a kite?

E

Find the angles marked with letters.�170°

120°110°

a

�2125°

60°

72°

b

�3 100°147°

36°

c d

20

�4 63°

132°e

f

�5142°

117° 71°

h

g

�6 42°

146°84°

66°

j

k

i

�7 67°

59°

168°

m

l

�8

19°

76°

74°

83°

n

�9 If —QRS = —RST = —STQ, find the

value of —RST.

132°

Q PR

ST

TASK 3.7

M

Find the angles marked with letters.

�1 41° 36°a

b

�2 62°

c d

�3

133°

f g

e�4 106°

123°

148°

i

h

21

�558°

49°

k

j

l

�639°

85°

mm

�7

78°

83°

64°

o

n

p

�8 152°

48°

28°

rq

s

E�1 Prove that triangle QRS is isosceles.

Give all your reasons clearly.

105°

30°

R Q P

S

�2 ABCD is a square.

Prove that triangle BCD is isosceles.

Give all your reasons clearly.

A B

D C

�3 Prove that triangle QUT is isosceles.

Give all your reasons clearly.

WT

UX V

R

PS

Q116°

64°

�4 Prove that the sum of the angles in a triangle add up to 180�.

Give all your reasons clearly.

�5 ABCD is a rectangle.

Prove that triangle ABM is

isosceles.

Give all your reasons clearly.

CD

A B

M2 cm

2 cm 2 cm

2 cm

22

TASK 3.8

M only�1 Copy and complete the sentence:

‘The exterior angles of a polygon add up to .’

�2 An octagon has 8 sides. Find the size of each exterior angle of a

regular octagon.

�3 A decagon has 10 sides.

a Find the size of each exterior angle of a regular decagon.

b Find the size of each interior angle of a regular decagon.

�4 Find the size of angle a.

a

(9 sides)

�5 Find the exterior angles of regular polygons with

a 18 sides b 24 sides c 45 sides

�6 Find the interior angle of each polygon in Question�5 .

�7 The exterior angle of a regular

polygon is 24�. How many sides

has the polygon? 24°

interior angle

�8 The interior angle of a regular polygon is 162�. How many sides has

the polygon?

ALGEBRA 1 4

TASK 4.1

M

In Questions�1 to�20 find the value of each expression when p = 4

q = 3

r = 7

23

�1 3p �2 qr �3 5p + 7 �4 2p + 5r�5 8q 2 2r �6 p2 �7 r 2 2q �8 r2

�9 q2 + r2 �10 8(p 2 q) �11 9(2r 2 p) �12 q(6p + 2q)

�13 r(3r 2 4q) �148q

p �15 9q + 6 �162p + 2q

r

�176(p + q)

r �18 p2 + q2 + r2 �19 pqr �20 5p + 6q 2 3r

In Questions�21 to�23 find the value of each expression:�21 20 2 2y if y = 5 �22 9(3a + 1) if a = 2 �23 8m + m2 if m = 4

E

In Questions�1 to�20 find the value of each expression when f = 21

g = 5

h = 24�1 2h �2 3f �3 fg �4 f h�5 2g 2 h �6 3f + 4g �7 4f + 3g �8 h2

�9 g2 + h2 �10 16 2 h �11 f + g + h �12 5g + 6f�13 6h + 10 �14 3( f + g) �15 7(g 2 f ) �16 (4f )2

�17 4g 2 3f + 3h �18 6h

2f �197(f + g)

h �20 2h2

In Questions�21 to�23 find the value of each expression:�21 3b + 6 if b = 22 �22 4(2 2 3x) if x = 26 �23 9(n2 2 20) if n = 25

TASK 4.2

M�1 c = 4d 2 3 �2 y = 5x + 6

Find c when d = 5. Find y when x = 7.

�3 m =p

42 8 �4 A = 6(B + 2)

Find m when p = 40. Find A when B = 7.

�5 V = IR

Find V when I = 7 and R = 15.

�6 f = 2u

v

Find f when u = 16 and v = 4.

�7 y = 5(2x + 6y)

Find y when x = 4 and y = 7.

�8 P =Q

6+ 4R

Find P when Q = 48 and R = 13.

24

�9 A = r2 + wr Use a calculator to find the value of A

when r = 3·6 and w = 1·4.

�10 V = lwh + 4wh Use a calculator to find the value of V

when l = 8·4, w = 0·9 and h = 3·8.

E�1 Below are several different formulas for p in terms of n. Find the

value of p in each case.

a p = 8n + 7 when n = 0·5

b p = 6(4n 2 1) when n = 5

c p = 3n

2+ n2 when n = 6

�2 The total surface area A of this cuboid is given by the formula

A = 2lw + 2lh + 2hw

h

w

l

Find the value of A when

a l = 5, w = 3 and h = 1

b l = 10, w = 2·5 and h = 4

�3 Find the value of y using formulas and values given below:

a y = 4x + c when x = 17 and c = 23

b y = x2 2 b when x = 23 and b = 2

c y = x

9+ z

4when x = 54 and z = 68

d y = x2 + 8x when x = 210

�4 The surface area A of a sphere is given by the

formula A = 12r2

Find the value of A when

a r = 3 b r = 5 c r = 8

�5 Energy E is given by the formula E = mc2 where m is the mass

and c is the speed of light.

Find the value of E when m = 15 and c = 300 000 000.

�6 Using the formula M = 7P 2 Q, find the value of M when

a P = 28 and Q = 19 b P = 215 and Q = 288

25

TASK 4.3

M

Collect like terms�1 9x + 4y + 5y �2 5p + 6q + 3p �3 8a + 2b + 4b + 5a�4 4m 2 2m + 8p + p �5 4a + 6b 2 b �6 4f + 3f + 6g 2 5f�7 3a + 6b + 3b 2 4b �8 9p 2 4p + q �9 4m + 6q 2 3q 2 2m�10 5a + 8b 2 7b 2 4a �11 2x 2 x + 6y 2 y �12 5m + 2p 2 3m + 9q 2 p

�13 Copy and complete the pyramids below. The answer for each box is

found by adding the 2 boxes below it.

a

2a + b

2a 3ab

b

3x x2y 5y

c 13p + 17q

7p + 10q

5q + 3p

4p 3p

E

Simplify�1 25b + 2b �2 24x + 9x �3 27y + 5y�4 3p 2 6p + 9q �5 4a + 7b 2 b 2 6a �6 5x + 2 + 3x�7 5c + 2 2 8c + 1 �8 6 + 3m 2 5m �9 3f + 6f + 4�10 7a2 + 3a2 + 5a2 �11 8x2 2 6x2 + x2 �12 5ab + 10ab 2 7ab�13 12xy + 3x 2 6xy �14 9mn + 4 + 3mn �15 6p2 2 p�16 5m2 2 3m + 4m2 �17 a + b + ab + 4a �18 4a2 + 6ab 2 4ab + 3a2

�19 The expression in each bag

shows how much money

is in it. Find and simplify

an expression for the

money Jack spends if he

uses all the money in:

6pq + 3

A

2 − 4pq

B

8p + 4

Ca bags A and B

b bags A and C

c all 3 bags

26

�20 Darryl is (4a2 + 6ab) years old. Christine is (3a + 2ab) years old and

Rory is (ab 2 a2) years old. Find and simplify an expression for their

total ages.

TASK 4.4

M

Do the following multiplications and divisions:�1 3a · 3 �2 2b · 4 �3 7m · 3 �4 5 · 7n�5 6 · 8y �6 16x 4 2 �7 27y 4 3 �8 60a 4 10�9 12b 4 4 �10 8m · 5 �11 n · n �12 y · y�13 6a · a �14 9f · f �15 q · 7q �16 3y · 2y�17 5b · 3b �18 8m · 4p �19 5a · 9b �20 10a · 10a

E

In Questions�1 to�9 answer ‘true’ or ‘false’.�1 a + b = ab �2 a + a = a2 �3 5m + m = 6m�4 6n2 2 n2 = 6 �5 4y · y = 4y2 �6 7a · 2b = 14ab�7 16x 4 4 = 12x �8 a · 5 · b = 5ab �9 y · y · y = y3

Simplify�10 4a · 26b �11 23m · 22p �12 26a 4 23�13 215x 4 5 �14 25a · 22a �15 29f · 24g�16 23p · 7q �17 8a · 24c �18 2a · 3a�19 26y · 11 �20 3b · 26b �21 242a2 4 22

TASK 4.5

M

Copy and complete:�1 3(a + 4) = + 12 �2 a(a + b) = a2 +

Multiply out�3 5(m + 2) �4 4(x 2 3) �5 6(a 2 8)�6 2(3y + 5) �7 9(2m 2 4) �8 3(x + y)�9 6(2a 2 b) �10 5(m + 3p) �11 7(2x + 5)

27

�12 4(3p 2 4q) �13 a(b + c) �14 x(x 2 y)�15 m(m 2 3p) �16 c(2d + 1) �17 2p(p + q)

Write down and simplify an expression for the area of each shape below:

�18 2a + b

5

�19 4b − 1

a

�20 m + 8p

m

E

Copy and complete:�1 24(x + 7) = 2 28 �2 23 (6b 2 2) = 218b +

Expand�3 23(a + 2) �4 26(b 2 4) �5 25(x 2 3)�6 22(3m 2 4) �7 2a(b 2 c) �8 2m(2 2 p)�9 2y(x + z) �10 2x(x + 3y) �11 2(a 2 b)�12 2(p + q) �13 2b(2a 2 3) �14 2f(5g + 2h)�15 2q(q 2 8r) �16 3a(3a + 4b) �17 28x(4x 2 3y)

TASK 4.6

M

Copy and complete:�1 3(4a + 7) 2 5a = + 21 2 5a = + 21

�2 5(4x + 6) + 3(2x 2 5) = + 30 + 2 15 = + 15

Simplify�3 3(a + 4) + 7 �4 6(m + 4) 2 9�5 5(x + 6) + 3x �6 2(4y + 7) + 12�7 9(2b + 4) + 4b �8 7(5a + 6) 2 10a

Expand and simplify�9 3(x + 4) + 4(x + 2) �10 2(4p + 3) + 5(p + 3)�11 6(2m + 5) + 3(4m + 1) �12 7(3a + 2) + 4(a 2 2)

28

�13 3(8y + 6) + 2(2y 2 5) �14 5n + 9 + 6(2x + 3)�15 4b + 9(3b + 6) 2 24 �16 7(4c + 7) + 3(2c 2 8)

E

Copy and complete:�1 6(3a + 2) 2 4(2a + 2) = + 12 2 2 8 = + 4

�2 7(4x + 3) 2 5(3x 2 6) = 28x + 2 15x + = 13x +

Simplify�3 5(a + 4) 2 3(a + 2) �4 6(2m + 3) 2 5(m + 3)�5 8(2x + 5) 2 4(x 2 2) �6 4(6p + 4) 2 3(3p 2 5)�7 4(5y + 6) 2 2(4y + 3) �8 2(8b + 9) 2 4(4b 2 6)�9 8a 2 3(2a 2 5) + 6 �10 7x 2 4(x 2 1) 2 3�11 9(4n + 7) 2 5(2n + 4) �12 10q + 3(5 2 2q) + 4(7q + 4)

TASK 4.7

M�1 Copy and complete the following:

a (x + 2) (x + 5) b (x + 7) (x + 3) c (x + 8) (x + 2)

= x2 + 5x + + 10 = x2 + + 7x + = + + 8x + 16

= x2 + + 10 = x2 + + = + + 16

Multiply out the following:�2 (x + 4) (x + 6) �3 (m + 7) (m + 5) �4 (y + 10) (y + 4)�5 (n + 6) (n + 7) �6 (a + 2) (a + 9) �7 (x + 12) (x + 3)

�8 Work out the area of this square,

giving your answer in terms of x.

x 4

x

4

Expand:�9 (x + 6) (x + 6) �10 (x + 7)2 �11 (x + 1)2

29

E�1 Copy and complete the following:

a (x + 3) (x − 5) b (y − 4) (y − 4) c (n − 8) (n + 5)

= x2 2 + 3x 2 15 = y2 2 2 4y + = + 5n 2 2 40

= x2 2 2 15 = y2 2 + = 2 2 40

Expand:�2 (x + 4) (x 2 6) �3 (a 2 6) (a 2 5) �4 ( y 2 3) ( y 2 7)�5 (n 2 9) (n + 4) �6 (m + 7) (m 2 6) �7 (b + 5) (b 2 8)�8 (a 2 8) (a 2 8) �9 (x 2 3) (x 2 4) �10 ( f + 10) ( f 2 7)

Multiply out the following:�11 (n 2 5) (n 2 5) �12 (y 2 7)2 �13 (a 2 2)2

�14 (4 + x) (x + 7) �15 (p 2 3)2 �16 (m + 2) (8 2 m)

TASK 4.8

M

Copy and complete�1 4a + 6 = 2(2a + ) �2 6a + 2 = 2(3a + ) �3 6m 2 9 = 3(2m 2 )�4 18b 2 12 = 6( 2 2) �5 16y + 28 = 4( + ) �6 40x 2 24 = 8( 2 )

Factorise the expressions below:�7 6x + 10 �8 8a + 12 �9 10p 2 40�10 20y 2 25 �11 12m + 9 �12 36b 2 12�13 9x + 6y �14 16a + 12b �15 24m 2 20p�16 45f + 35g �17 21a 2 15b �18 30x 2 50y�19 8p + 6q 2 10r �20 15x 2 30y 2 20z �21 35a 2 21b + 49c

E

Copy and complete�1 ab + af = a(b + ) �2 xy 2 xz = x( 2 z)�3 4mp 2 10m = 2m(2p 2 ) �4 n2 + 7n = n(n + )�5 f 2 2 9f = f ( 2 9) �6 4ab + 18bc = 2b( + )

Factorise the expressions below:�7 xy + yz �8 a2 2 6a �9 b2 + 4b�10 c2 + 9c �11 mp 2 pq �12 3xy + 9xz�13 10ab 2 15ac �14 18wz 2 15wy �15 12fg + 21f

30

�16 4a2 2 6a �17 5p2 2 30pq �18 18mp + 30m�19 8pq 2 20q2 �20 16xyz 2 28y2 �21 33a2 + 55abc

NUMBER 3 5

TASK 5.1

M�1 Copy each shape below and shade in the given fraction.

a

38

b

34

c

716

d

910

�2 Find 1

10of: a 30 b 80 c 100 d 500

�3 Find 1

7of: a 14 b 35 c 63 d 140

Work out:�4 1

5of 35 �5 2

3of 18 �6 3

8of 56 �7 5

7of 42

�8 There are 30 students in a class. 2

5of them are girls. How many girls are

there in the class?

�9 In a spelling test full marks were 54. How many marks did Simon get

if he got 5

6of full marks?

�10 Maddy has 12 pairs of shoes. 4 pairs of shoes are black.

a What fraction of her shoes are black?

b What fraction of her shoes are not black?

�11 In a food survey, 41 people were asked what their favourite meal was.

16 people chose ‘pizza’.

a What fraction of the people chose ‘pizza’?

b What fraction of the people did not choose ‘pizza’?

31

�12 What fraction of the months of the year begin with the letter J?

�13 There are 60 minutes in 1 hour.

What fraction of 1 hour is:12 1

3

2

4567

8

9

1011

a 10 minutes b 20 minutes

c 45 minutes d 50 minutes

e 17 minutes f 36 minutes

(Try and cancel your answers)

E

Work out�1 5

7of 63 �2 5

8of 24 �3 2

9of 72 �4 3

7of 42

�5 5

9of 27 �6 7

8of 64 �7 1

6of 126 �8 9

50of 400

�9 A toaster costs £25. In a sale, the price of a toaster is reduced by 2

5.

How much does a toaster cost now?

�10 A packet of biscuits contains 276 g. If a packet of biscuits now has

1

3extra, how much does it contain?

�11 In seven years, a footballer scored 216 goals and 2

9of these were

headers. How many headers did he score?

�12 A box of ‘Cleano’ now contains 2

3extra. Normally it contains 420 g.

How much does it have now?

�13 In a sale, a music system has 3

7knocked off the price. If it was

originally priced at £392, what does it cost in the sale?

TASK 5.2

M

Change the following improper fractions to mixed numbers.�1 8

3 �2 7

6 �3 14

5 �4 8

5= 1

5

�5 7

3=

3 �6 17

8= 2

8 �7 9

2 �8 13

3

�9 19

5 �10 31

4 �11 23

8 �12 40

9

32

E

Change the following mixed numbers to improper fractions.�1 12

5 �2 25

8 �3 35

6 �4 34

5= 19

�5 42

3=

3 �6 53

4=

4 �7 27

8 �8 45

6

�9 31

5 �10 93

4 �11 82

3 �12 93

8

In the Questions below, change improper fractions to mixed numbers

or mixed numbers to improper fractions.�13 47

8 �14 35

4 �15 26

5 �16 15

8 �17 62

3 �18 21

7

�19 95

6 �20 23

7 �21 82

9 �22 21

7 �23 47

9 �24 65

8

TASK 5.3

M

Work out�1 1

4+ 2

4 �2 8

92

7

9 �3 8

112

5

11 �4 7

20+ 4

20

�5 Tim ate 3

7of his pizza and gave 2

7of his pizza to his sister who ate

it straight away. What total fraction of the pizza has been eaten?

�6 Mr. Agg gave 4

9of his money to his son and 4

9of his money to his

daughter. In total, what fraction of his money did he give away?

�7 Copy and complete:

a 2

7+ 3

8b 5

62

1

4c 7

102

2

9

=56

+56

=12

212

=90

2

=56

= =

In Questions�8 and�9 , which answer is the odd one out?�8 a 5

62

5

12b 1

3+ 1

4c 2

32

1

12

�9 a 1

4+ 1

16b 11

162

3

8c 3

16+ 5

8

33

�10 Tanya gives 1

3of her clothes to her sister and 1

10of her clothes to a

cousin. What fraction of her clothes did Tanya give away in total?

�11 In a class, 1

4of the students come by bus and 3

5of the students walk. The rest

of the students come by car. What fraction of students come by car?

�12 Work out

a 41

2+ 22

3b 33

4+ 23

4c 73

4+

7

10d 13

8+ 61

3

�13 I travel along the road from A to C.

What is the total distance I travel?A

B

C

3 km14

5 km23�14 Which answer is the odd one out?

a 31

62

3

4b 3 3

102 11

3c 43

42 21

3

1 m34

1 m110

?

�15 Joynul has a 13

4metre length of wood. He cuts off 1 1

10metre

of the wood. What length of wood has he got left?

E

Work out (cancel your answers where possible)�1 1

2of 1

3 �2 1

3of 1

5 �3 3

4of 1

2 �4 2

3of 3

5

�5 1

4· 1

8 �6 1

7· 1

6 �7 1

4· 2

7 �8 3

5· 2

9

�9 3

4· 6 �10 5

6· 4 �11 5

8· 10 �12 2

3· 6

�13 Find the area of each of the 3 rooms below:

a 6 m23

4 m12

b 3 m34

5 m45

c 8 m14

4 m23

34

Work out, cancelling where possible:

�14 10 41

2 �15 6 41

3 �16 1

74 1

4 �17 1

24

1

3

�18 2

94 1

4 �19 3

74 2

3 �20 2

114 8

9 �21 9

204 3

4

�22 Match each Question to the correct answer (one answer is an odd

one out):

2 ÷14

716

1 ÷ 112

38

4 ÷ 213

34

5 17P

11933Q

1 415R

1 111S

A

B

C

�23 How many whole rods of length 3

16m can be cut from a pole of

length 9

10m ?

NUMBER 4 6

TASK 6.1

M�1 In a survey 73 out of every 100 people said they loved ice cream. Write

down the percentage of people who love ice cream.

�2 45% of the students in a class said they had been to the cinema in the

last month. What percentage of the students had not been to the cinema

in the last month?

�3 68% of men drink alcohol at least once during the week. What

percentage of the men do not drink alcohol at least once during the

week?

35

�4 a What percentage of the large square is shaded?

b What percentage of the large square is not shaded?

�5 53 out of every 100 children walk to school each day.

What percentage of children do not walk to school?

E�1 Change these percentages into fractions. Cancel the answers when

possible�

example: 46% = 46

100=

23

50

�.

a 17% b 20% c 29% d 12% e 25% f 60%

g 24% h 35% i 88% j 32% k 9% l 95%

�2 2% of semi-skimmed milk is fat. What fraction of semi-skimmed milk is fat?

�3 Change these fractions into percentages (remember: multiply by 100

unless you can see a quicker way).

a 7

10b 2

5c 3

25d 38

50e 13

20f 8

25

�4 Elmer scored 17 out of 20 for English coursework. What percentage was this?

TASK 6.2

M�1 19 out of 20 pupils in a class go on a school trip. What percentage

of the class go on a school trip?

�2 What percentage of these boxes contain:

a crosses

b circles

36

�3 a Write 19 as a percentage of 50.

b Write 11 as a percentage of 20.

c Write 300 as a percentage of 500.

�4 In a survey 120 people were asked if they had internet access at home. 96 people

said ‘yes’. What percentage of the people said they had internet access at home?

�5 150 students were asked where

their home town was. The findings

are shown in this table.

What percentage of the students

came from:

a Wales b The North

c Ireland d The Midlands

home area

number of

students

Wales 45

The South 24

The Midlands 27

The North 36

Scotland 6

Ireland 12

Total 150

E

Use a calculator for the Questions below. Give your answers to the

nearest whole number.�1 28 out of 43 young people at a Youth club one evening are male.

What percentage of the young people are male?

�2 Sunita is given £60 for her birthday. She spends £47 on computer

games. What percentage of her birthday money has she got left?

�3 What percentage of these letters is the

letter ‘K’?O

O OO O

O OK K K

KK K K

K

�4 Tamsin scored 39 out of 47 in a Science test. Peter scored 47 out of 58 in his

Science test. Who scored the higher percentage and by how much?

�5 The table shows how some of a 30 g

serving of sultana bran cereal is

made up.

What percentage of the 30 g

serving is:

fat 2·6 g

sugars 16 g

salt 0·5 g

saturated fat 1·4 g

a fat b sugars c salt d saturated fat

�6 The population of Glastonbury in Somerset is about 10 000. The population

of the UK is about 60 000 000. What percentage of the UK’s population

live in Glastonbury (give your answer to 2 decimal places)?

37

TASK 6.3

M�1 Find 25% of:

a 60 b 24 c 44 d 120 e 36

�2 Find 331

3% of:

a 15 b 27 c 90 d 54 e 75

�3 Find 20% of:

a 40 b 200 c 140 d 30 e 90

�4 Find 15% of:work out 10% and

5% then add

together

a 40 b 140 c 300 d 70 e 10

�5 60% of adults have a mobile phone. If 210 adults were asked,

how many would have a mobile phone?

�6 Terry earns £260 a week. Each week he gives 5% of his

money to charity. How much money does he give

each week?

�7 Find the odd one out

a 30% of £30 b 5% of £160 c 25% of £32

E

Use a calculator when needed.�1 Find 1% of:

a 700 b 250 c 87 d 460 e 6

�2 Find 4% of:

a 300 b 900 c 350 d 75 e 5

�3 Find 17·5% of:

a 400 b 320 c 48 d 680 e 8

�4 60 people eat at a restaurant one evening. 55% of these people

eat fish. How many people do not eat fish?

�5 Find the odd one out

a 6% of 34 b 14% of 26 c 8% of 45·5

�6 The garages of 1600 houses were examined. 23% of the garages

had yellow doors. How many garages had yellow doors?

�7 Work out, correct to the nearest penny:

a 13% of £24·20 b 37% of £41·60

c 19% of £36·14 d 4·8% of £83

38

TASK 6.4

M

Do not use a calculator.�1 a Increase £40 by 10%. b Decrease £70 by 20%.

c Decrease £50 by 40%. d Increase £28 by 75%.

�2 Kate earns £340 each week. She is given a pay rise of 5%.

How much does she now earn each year?

�3 A laptop costs £1240. One year later it costs 20% less. How much

does the laptop cost now?

�4 What is the sale price of each item below?

aSofa £800

SALE30% off

b

Dishwasher £480SALE

25% off

cDVD player £60

SALE15% off

�5 A car costs £24 000. A year later its price has decreased by 3%.

How much does the car cost now?

�6 Increase £800 by 17·5%.Find 10% then 5%

then 2·5% and add

them all together

�7 VAT is value added tax. This tax is added to the cost of items. VAT

is usually 17·5%.

a Find 17·5% of £360.

b Find the cost of a washing machine which costs £360 + VAT.

E

Use a calculator when needed. Give answers to the nearest penny

when needed.�1 a Decrease £70 by 3%. b Increase £68 by 2%.

c Decrease £264 by 46%. d Increase £89 by 12%.

�2 Carl’s caravan is worth £15 500. One year later it is worth 6%

less. How much is the caravan now worth?

�3 A cinema increases its prices by 8%. If a ticket was £6·50, what

would it cost after the increase?

�4 A tin of baked beans costs 42p. Its price increases by 9% over the

next 12 months. How much will the tin cost now? (remember to

give your answer to the nearest penny)

39

�5 A new car exhaust costs £88 + VAT. If VAT is 17·5%, work out

the total cost of the car exhaust.

�6 A new dining table costs £450 + VAT. If VAT is 17·5%, work out

the total cost of the dining table.

�7 If VAT is 17·5%, find the price including VAT of each of the

following:

a microwave £126 b carpet £870

c digital camera £220 d kettle £34

�8 An eternity ring costs £680 + VAT (17·5%).

a What is the total price of the ring?

b In the Summer sales, the price of the ring is reduced by 20%.

How much does the ring cost in the sales?

TASK 6.5

M�1 Change these percentages into decimals:

a 47% b 21% c 80% d 36% e 4% f 7%

�2 Change these decimals into percentages:

a 0·59 b 0·23 c 0·03 d 0·3 e 0·2 f 0·18

�3 Match up equivalent fractions, decimals and

percentages. (You should find 5 groups of

3 numbers and there is one number

on its own)

25

14

34

7109

10025%

70%

9% 40%

75%

0·34 0·75

0·090·25

0·70·4

E

Use a calculator when needed. Give answers to the nearest whole

number when needed.�1 Ryan buys a mobile for £240 and sells it one year later for £204.

What was his percentage loss?

�2 Kelly buys a car for £300 and works on it before selling it for

£420. What was the percentage profit?

40

�3 A supermarket increases its workforce from 90 people to

117 people. What is the percentage increase?

�4 Find the percentage increase or decrease for each of the following:

a original amount = 360 final amount = 514·8

b original amount = 672 final amount = 564·48

c original amount = 32 final amount = 62·4

�5 In 2005, a company makes a profit of £3 million. In 2006, the

company makes a profit of £4 million. What is the percentage

increase in the profit?

�6 Leanne buys 100 books for £450. She sells each book for £5·40.

Find the percentage profit Leanne makes on the books.

�7 Sam buys 70 scarves at £5 each. He sells 40 of the scarves for £11

each but fails to sell the other scarves. Find the percentage profit

he makes.

�8 Joe buys a flat for £70 000 and sells it for £85 000.

Mo buys a house for £192 000 and sells it for £230 000.

Who makes the larger percentage profit and by how much?

TASK 6.6

M

Use a calculator when needed. Give answers to the nearest penny

when needed.�1 Tina invests £8000 in a bank at 5% per annum (year) compound

interest. How much money will she have in the bank after 2 years?

�2 £12 000 is invested at 10% per annum compound interest. How

much money will there be after 2 years?

�3 A motorbike loses 25% of its value every year. Jennifer bought it

for £720. How much would it be worth after:

a 2 years b 3 years

�4 Tom buys a guitar for £400. Each year it loses 15% of its value at

the start of the year. How much would the guitar be worth after:

a 2 years b 3 years�5 A bank pays 7% per annum compound interest. How much will the

following people have in the bank after the number of years stated?

a Callum: £5000 after 2 years b Megan: £3500 after 2 years

c Lauren: £20 000 after 3 years d Oliver: £900 after 2 years

41

�6 Which of the following will earn more money in 2 years?

a £4000 at 5·6% p.a. simple interest or

b £4000 at 5·5% p.a. compound interest and by how much?

E�1 A bank pays 4% p.a. (per annum) compound interest. Use the

percentage multiplier 1·04 (100% + 4% = 104%) to find how much

money would be in the bank after 3 years if Jack invested £1500.

�2 A building society offers 8% p.a. compound interest. Candice puts

£560 into the building society.

a Write down the percentage multiplier which could be used to

find out how much money is in the building society after 1 year.

b How much money would be in the building society after

5 years?

�3 The population of a small town increases by 14% each year. At

the end of year 2001, the town’s population was 2600.

Copy and complete the table below, giving your answers to the

nearest whole number.

end of year population

2002

2003

2004

2005

2006�4 What is the percentage multiplier to find out how much is left

after a 21% decrease. what percentage

would you have

left after you have

taken off 21%?�5 A boat is worth £28 000. Its value depreciates (goes down) by 12%

of its value each year. How much will the boat be worth after:

a 3 years b 10 years

�6 The value of a house increases by 9% of its value each year. If a

house is worth £170 000, how much will it be worth after:

a 2 years b 7 years c 20 years

TASK 6.7

M�1 Copy and complete each sentence below:

aThe ratio of black to white is :

bThe ratio of black to white is :

42

�2 For each diagram below, write down the ratio of black to white in

its simplest form.

a b

�3 Copy the diagrams and colour them in to match the given ratio.

aThe ratio of black to white is 2 : 3.

bThe ratio of black to white is 2 : 1.�4 In a swimming pool there are 30 people. 20 of the people are male.

Find the ratio of males to females. Give the ratio in its simplest form.

�5 In a box there are 14 pens and 6 pencils. Find the ratio of pens to

pencils in its simplest form.

�6 The ratio of boys to girls in a class is 3 : 4. If there are 12 boys,

how many girls are there?

�7 The ratio of blond haired people to dark haired people is 5 to 2. If there

are 6 dark haired people, how many blond haired people are there?

�8 Change the following ratios to their simplest form.

a 8 : 10 b 30 : 40 c 12 : 30 d 63 : 27

e 32 : 28 f 12 : 9 : 21 g 50 cm : 4 m h 25p : £3

E�1 5 lemons cost 95p. What do 3 lemons cost?

�2 4 Kiwi fruit cost 84p. What do 6 kiwi fruit cost?

�3 7 books cost £42. How much will 9 books cost?

�4 8 hats cost £56. How much will 7 hats cost?

�5 3 dishwashers cost £1245. What do 5 dishwashers cost?

�6 4 calculators cost £23·96. How much will 7 calculators cost?

�7 13 people pay £89·70 to visit a castle. How much would

28 people have to pay?

�8 Mindy used 550 g of lamb to make a curry for 8 people. How

much lamb would she have to use to make curry for 12 people?

�9 Cheese kebabs for 4 people need the ingredients below:

220 g cheese

4 tomatoes

8 pineapple chunks1

2cucumber

How much of each ingredient is needed for 10 people?

43

�10 The recipe for making 20 biscuits is given below:

120 g butter

50 g caster sugar

175 g flour

How much of each ingredient is needed for 24 biscuits?

TASK 6.8

M�1 a Divide £150 in the ratio 1 : 4 b Divide £60 in the ratio 3 : 2

c Divide 49 g in the ratio 2 : 5 d Divide 96 kg in the ratio 5 : 3

e Divide £900 in the ratio 6 : 1 : 3 f Divide 75 litres in the ratio 4 : 5 : 6

�2 Todd and Claire receive a total of 30 christmas presents in the ratio

3 : 7. How many presents do each of them receive?

�3 A man leaves £12 000 to Carl and Rachel in the ratio 5 : 1. How

much will each person get?

�4 The angles p, q and r are in the ratio 7 : 2 : 3.

Find the sizes of angles p, q and r.

p q

r

�5 There are 45 000 fans at a football match involving Aston Villa and

Birmingham City. The ratio of Aston Villa fans to Birmingham City

fans is 5 : 4. How many Aston Villa fans are at the football match?

E�1 The ratio of boys to girls in a class is 6 : 5. How many girls are

there in the class if there are 18 boys?

�2 Paint is mixed by using yellow and blue in the ratio 7 : 2.

a How much yellow is used if 8 litres of blue are used?

b How much blue is used if 35 litres of yellow are used?

c How much yellow and how much blue must be used to make

72 litres of the paint?

�3 Some money is left to Will and Dido in the ratio 9 : 11. If Will

gets £1080, how much will Dido get?

44

�4 Orange squash is diluted with water in the ratio 1 : 7.

a If 12 ml of orange squash is used, how much water should be

added?

b If 72 ml of water is used, how much orange squash should be

added?

�5 Des, Simone and Julie earn money in the ratio 3 : 2 : 5. If Des earns

£27 000 each year, how much do Simone and Julie each earn?

�6 Ginny and Ben have collected ‘Warhammer’ pieces in the

ratio 7 : 4. If Ginny has 63 pieces, how many pieces do they

have in total?

�7 The ratio of weeds to flowers in a garden is 8 : 5. If there are

280 weeds in a garden, how many flowers are there?

�8 Ellie, Dan and Lewis own CD’s in the ratio 14 : 5 : 9. If Lewis

owns 81 CD’s, how many CD’s do they own in total?

SHAPE 2 8

TASK 8.1

M

Use tracing paper if needed.�1 Which shapes are congruent to shape A?

A B

C D E

�2 Which shapes are congruent to shape P?

P QR

S

T

45

�3 Which 2 shapes are congruent?

A

B

C

DE

�4 Which shapes are congruent to:

a shape A b shape B

c shape E d shape F A

BC D

GFE

H

K L

M

N

JI

E

can be split intotwo congruent shapes

Copy each shape below then show how each shape can be split into the

congruent shapes.

�1 �2 �3

46

�4 �5 �6

�7 �8

TASK 8.2

M�1 a Use this grid to spell out this message.

(4, 1) (3, 4) (1, 3) (4, 5)

(1, 1) (3, 4)

(4, 2) (2, 2) (1, 5)

5

4

3

2

1

00 1 2 3 4 5

T P

EKB

L C I

OUQ

M S H

YN

b Use co-ordinates to write

the word SENSIBLE.

�2 Draw a horizontal axis from 0 to 16.

Draw a vertical axis from 0 to 16.

Plot the points below and join them with a ruler in the order given.

(4, 9) (1, 11) (3, 8) (1, 5) (4, 7) (6, 5) (7, 5) (8, 3)

(9, 5) (11, 5) (12, 7) (15, 9) (15, 10) (12, 11) (9, 11) (8, 14)

(7, 11) (6, 11) (4, 9)

�9

47

On the same picture plot the points below and join them up with a

ruler in the order given. Do not join the last point in the box above

with the first point in the new box.

(15, 12) (16, 12) (16, 13) (15, 13) (15, 12)

(14, 14) (13, 14) (13, 15) (14, 15) (14, 14)

(12, 8) (13, 8)

Draw a � at (13, 10) Colour in the shape?

E�1 Draw a horizontal axis from 25 to 12.

Draw a vertical axis from 25 to 12.

Plot the points below and join them with a ruler in the order given.

(0, 24) (1, 1) (1, 22) (2, 23) (1, 23) (0, 24)

On the same picture plot the points below and join them up

with a ruler in the order given. Do not join the last point in the

box above with the first point in the new box.

(3, 6) (3, 3) (5, 5) (6, 7) (6, 10)

(23, 9) (24, 9) (24, 10) (23, 10)

(7, 24) (6, 23) (5, 23) (5, 21) (4, 1) (3, 2) (2, 5)

(3, 6) (4, 8) (6, 10) (5, 12) (3, 12) (2, 11) (21, 11)

(23, 10) (23, 9) (22, 8) (0, 8) (1, 7) (21, 2) (21, 23)

(22, 23) (23, 24) (7, 24)

(2, 11) (2, 10) (0, 8) (1, 8) Colour me in?

�2 Draw a horizontal axis from 210 to 8.

Draw a vertical axis from 210 to 8.

Plot the points below and join them with a ruler in the order given.

(210, 27) (29, 26) (28, 24) (26, 22) (24, 22) (22, 21) (22, 21)

(3, 1) (2, 2) (2, 4) (4, 2) (5, 2) (7, 4) (7, 2)

(6, 1) (7, 0) (7, 21) (6, 21) (5, 22) (4, 21) (3, 21)

48

On the same picture plot the points below and join them up with a ruler in the order

given. Do not join the last point in the box above with the first point in the

new box.

(6, 21) (6, 23) (4, 25) (4, 29) (5, 29) (5, 24) (3, 26) (3, 29)

(2, 29) (2, 26) (1, 25) (21, 25) (2 1, 2 3½) (21, 26) (22, 27)

(22, 29) (23, 29) (23, 26) (24, 24) (24, 26) (25, 27) (25, 29)

(24, 29) (24, 27) (23, 26) (24, 24) (24, 23) (27, 28) (29, 28) (210, 27)

Colour me in?

TASK 8.3

M�1 Describe the following translations. In each case, write

down how many units left or right and how many

units up or down:

0123456789

0 1 2 3 4 5 6 7 8 9

B

A

CD

EF

G

x

y

a C to D b B to C

c E to F d A to B

e D to E f B to G

g G to F h F to C

�2 Copy the grid opposite and the rectangle A as shown.

a Translate rectangle A 2 units to the right and 2 units up.

Label the new rectangle B.

01234567

0 1 2 3 4 5 6 7

Ab Translate rectangle B 2 units to the right and 1 unit down.

Label the new rectangle C.

c Translate rectangle C 1 unit to the left and 3 units down.

Label the new rectangle D.

d Translate rectangle D 4 units to the left and 0 units up.

Label the new rectangle E.

e Translate rectangle E 6 units to the right and 1 unit up.

Label the new rectangle F.

f Describe the translation that moves rectangle D to

rectangle B.

g Describe the translation that moves rectangle E to

rectangle C.

49

E�1 Use translation vectors to describe the following

translations.

1−1−1

1

0

−2

2

−3

3

−4

4

−5

5

−2−3−4−5 2 3 4 5 x

y

AB

D

C

H

FE

G

a D to C b E to D

c A to B d E to F

e D to H f H to F

g E to B h E to G

i G to D j F to C

�2 Copy the grid opposite and draw shape A

as shown. Translate shape A by each of the

translation vectors shown below:

1−1−1

1

0

−2

2

−3

3

−4

4

−5

5

−2−3−4−5 2 3 4 5 x

y

Aa24

1

� �Label new shape B.

b1

23

� �Label new shape C.

c24

23

� �Label new shape D.

d21

25

� �Label new shape E.

e Use a translation vector to describe the

translation that moves shape D to E.

TASK 8.4

M

Draw each shape below and reflect in the mirror line.

�1 �2 �3

50

�4 �5 �6

�7 �8 �9

�10 �11 �12

E�1 Copy the grid and shape opposite.

1−1−1

1

0

−2

2

−3

3

−4

4

−5−6

56

−2−3−4−5−6 2 3 4 5 6 x

y

A

a Reflect shape A in the y-axis.

Label the image B.

b Reflect shape B in the x-axis.

Label the image C.

c Reflect shape C in the line x = 1.

Label the image D.

d Reflect shape D in the line y = 21·5.

Label the image E.

e Reflect shape E in the y-axis.

Label the image F.

f Reflect shape F in the line y = 2.

Label the image G.

g Shape G reflects back onto shape A.

Write down the name of the line

of reflection.

51

�2

1−1−1

1

0

−2

2

−3

3

−4

4

−2−3−4−5 2 3 4 5 x

y

A

B F

E

DC

For each pair of shapes below, write down the name of the line of reflection.

a A to B b A to C c C to D d D to E e E to F

TASK 8.5

M

Use tracing paper.

For each Question, draw the shape and the centre of rotation (C).

Rotate the shape as indicated and draw the image.�190° clockwiseC

�2

90° anticlockwiseC

�3

90° anticlockwise

C

�4

180°C

�5

90° clockwise

C

�6

90° anticlockwise

C

�7

180°

C �8

90° anticlockwise

C

52

�9 Find the co-ordinates of the

centres of the following

rotations:

a shape A onto shape B

b shape B onto shape C

c shape C onto shape D

D C

BA

00 1 2 3 4 5 6 7 8

12345678

y

x

E

Use tracing paper.�1 Describe fully the rotation which

transforms:

1−1−1

1

−2

2

−3

3

−4

4

−2−3−4 2 3 4 x

y

A B

CD

0

a triangle A onto triangle B

b triangle C onto triangle D

c triangle B onto triangle C

�2 a Draw the x axis from 26 to 5.

Draw the y axis from 26 to 7.

Draw rectangle A with vertices at

(2, 22), (3, 22) (3, 25) (2, 25).

b Rotate rectangle A 90� clockwise about (2, 21). Label the

image B.

c Rotate rectangle B 90� clockwise about (22, 22). Label

the image C.

d Rotate rectangle C 90� clockwise about the origin. Label the

image D.

e Rotate rectangle D 90� anticlockwise about (22, 2). Label

the image E.

f Rotate rectangle E 90� clockwise about (3, 2). Label the

image F.

g Describe fully the translation which transforms rectangle A

onto rectangle F.

53

TASK 8.6

M

Enlarge these shapes by the scale factor given. Make sure you leave room

on your page for the enlargement!�1scale factor 2

�2scale factor 3

�3scale factor 2

�4

scale factor 3

�5

scale factor 2

�6

scale factor 12

�7 Look at each of the following pairs of diagrams and decide whether or

not one diagram is an enlargement of the other. For each part, write the

scale factor of the enlargement or write ‘not an enlargement’.

a b

54

E

For Questions�1 to�3 , copy the diagram and then draw an enlargement

using the scale factor and centre of enlargement (C) given.

Leave room for the enlargement!�1

scale factor 3

�2

scale factor 2

�3

scale factor 2

For Questions�4 and�5 , draw the grid and the 2 shapes then draw

broken lines through pairs of points in the new shape and the old shape.

Describe fully the enlargement which transforms shape A onto shape B.

�4

1−1−1

1

2

3

4

5

6

−2 2 3 4 x

y

A

B

0

�5

1−1−1−2−3−4−5

12

3456

−2−3−4−5−6−7 2 3 4 x

y

A

B

0

�6 a Draw the x-axis from 26 to 10.

Draw the y-axis from 23 to 5.

Draw the shape A with vertices at (22, 2), (22, 3), (21, 3),

(21, 4), (24, 4), (24, 3), (23, 3), (23, 2).

b Enlarge shape A by scale factor 3 about (26, 4).

Label the image B.

c Enlarge shape B by scale factor 1

3about (23, 22).

Label the image C.

d Enlarge shape C by scale factor 1

2about (0, 0).

Label the image D.

55

TASK 8.7

You may use tracing paper.

M�1 Copy the shape and the mirror line.

a Reflect this shape in the mirror line.C

b Rotate this shape 90� anticlockwise

about the point C.

�2 Copy the shape.

a Rotate this shape 90� clockwise

about the point C.

C

b Translate the image 3 units to

the left and 2 units up.

�3 a Describe fully the rotation which

moves shape A onto shape B.

b Describe fully the translation which

moves shape B onto shape C.

0

1

2

3

4

5

6

0 1 2 3 4 5 6

B

A

Cx

y

c Describe fully the rotation which

moves shape C onto shape A.

56

E�1 Describe fully the transformation

which moves:

a triangle A onto triangle B

b triangle B onto triangle C

c triangle C onto triangle D

d triangle D onto triangle E

e triangle D onto triangle F 1−1−1

1

0

−2

2

−3

3

−4

4

−2−4−5 2 3 4 5 6 x

y

A

EC

F

B

D−3

�2 a Draw the x-axis from 25 to 5.

1−1−1

1

0

−2

2

−3

3

−4

4

−5−6

56

−2−3−4−5 2 3 4 5 x

y

A

Draw the y-axis from 26 to 6.

Draw shape A with vertices at (22, 2), (24, 2),

(24, 4), (22, 6).

b Enlarge shape A by scale factor 1

2about

the origin. Label the image B.

c Reflect shape B in the line y = 21.

Label the image C.

d Rotate shape C 90� anticlockwise about

(22, 22). Label the image D.

e Translate shape D through3

4

� �:

Label the image E.

f Rotate shape E 90� clockwise about (2, 2).

Label the image F.

g Describe fully the transformation that would

move shape F onto shape C.

NUMBER 5 9

TASK 9.1

M�1 Work out

a 7·6

+ 4·2

b 2·64

+ 5·18

c 19·7

2 12·4

d 6·28

21·6

57

e 13·0

2 7·4

f 14·68

+ 29·31

g 89·53

2 28·29

h 24·7

8·2

+ 37·43

�2 Write down which sets of numbers below add up to 14.

A 3·6 + 7·1 + 3·3 B 8 + 1·9 + 4·1

C 5·8 + 6·4 + 2·8 D 3·12 + 6 + 4·88

�3 Which answer below is the larger?

A 8·12 2 5·6 or B 7·36 2 4·74

�4 Work out the following (Remember to line up the decimal point):

a 4 + 2·17 b 6·84 + 2·19 c 51·4 2 17·6

d 28·6 2 15 e 49·81 2 16·9 f 19 2 4·8

E�1 How much change from a £10 note do you get if you spend:

a £4·81 b £2·64 c £8·21 d £6·72

�2 Denise has £20. She spends £3·25 on the bus and £4·83 on lunch. How much money

does she have left?

�3 Barney can spend up to £1200 on his credit card. He buys a laptop for £895·99,

a desk for £104·95 and a computer game for £34·50. How much more money

could he spend using his credit card?

�4 Which answer below is the smaller?

A 5 2 2·42 or B 19 2 16·52

�5 3·6 km 7·39 km

4 kmKemble

Dunton

Cowley Horwick

How far is it from Kemble to Horwick?

�6 Work out

a 216·4 2 83·26 b 18·7 + 45 + 13·18

c 51·8 2 27·27 d 5·187 2 2·43

58

�7 Find the perimeter of this pentagon. 5 cm

6·7 cm

8·4 cm12·87 cm

9·26 cm

�8 Find the difference between 46 and 17·48.

�9 Colin runs a race in 47·28 seconds. Donna runs the race in 51·1 seconds.

By how many seconds did Colin win the race?

TASK 9.2

M�1 Work out

a 7·418 · 100 b 0·63 · 100 c 8·94 · 10 d 5·234 · 1000

e 5·29 · 1000 f 0·4 · 100 g 7·164 · 10 h 8·2 · 1000�2 Copy and fill in the boxes

a 3·498 · = 34·98 b 0·81 · = 81 c · 100 = 3·6

d · 1000 = 14·6 e 0·0913 · = 91·3 f · 10 = 0·2

�3 Work out

a 6 · 0·1 b 29 · 0·01 c 0·4 · 0·1 d 13 · 0·1

e 0·71 · 0·1 f 48 · 0·01 g 631 · 0·01 h 0·8 · 0·1

�4 Copy and fill in the empty boxes

a 5·6 · = 0·56 b 384 · = 3·84 c 82 · = 0·82

d 3·9 · = 0·039 e · 0·1 = 0·6 f · 0·01 = 0·34

E�1 For each Question below write ‘True’ or ‘False’

a 0·6 · 0·3 = 0·18 b 0·8 · 0·6 = 0·48

c 0·4 · 0·08 = 0·032 d 8 · 0·05 = 0·4

�2 Work out

a 7 · 0·3 b 0·7 · 0·5 c 0·9 · 0·3

d 0·06 · 0·9 e 0·08 · 7 f 0·42

�3 Work out

a £1·76 · 3 b £3·64 · 4 c £7·13 · 8

59

�4 Find the total cost of 4 packets of washing powder at £3·28 for each packet.

�5 5 people each weigh 68·7 kg. What is their total weight?

�6 Which answer below is the correct answer?

A 1·8 · 0·7 = 1·26 or B 1·8 · 0·7 = 12·6

�7 Work out

a 5·9 · 0·4 b 26 · 0·07 c 34 · 0·03

d 0·17 · 0·5 e 1·3 · 0·08 f 2·51 · 0·9

�8 £1 = e1·68. Change £15 into Euros by multiplying by 1·68.

TASK 9.3

M�1 Work out

a 4Þ24.8 b 6Þ12.84 c 4Þ32.20

d 5Þ28.0 e 2Þ19.0 f 8Þ13.000

�2 Divide the following numbers by 4

a 9·52 b 23 c 55 d 4·5

�3 Maggy, Jack, Janet and Wasim go to a rock concert. The total cost of

the tickets is £62·60. What is the cost of one ticket?

�4 6 cars of beer cost £6·48. How much does one can of beer cost?

�5 Work out

a 11·4 4 6 b 30·7 4 5 c 41·92 4 8

d 34·48 4 4 e 4·83 4 7 f 0·234 4 9

�6 A multipack of tins of baked beans costs £1·56. The multipack

contains 4 tins of baked beans. A single can of baked beans can be

bought for 45p each. Which is the better price for one tin of baked

beans and by how much?

E�1 Copy the Questions below and fill in the empty boxes.

a 13·2 4 0·4 = 132 4 4 =

b 5·84 4 0·2 = 58·4 4 =

c 7·1 4 0·02 = 710 4 =

d 15·6 4 0·02 = 4 2 =

60

�2 Work out

a 1·35 4 0·3 b 6·8 4 0·2 c 3·36 4 0·6

d 0·192 4 0·4 e 0·215 4 0·05 f 0·504 4 0·08

�3 A bottle contains 0·12 litres of medicine. A teaspoon holds 0·005

litres. How many teaspoons of medicine can be taken from the bottle?

�4 Copy and complete the number chains below:

a 6·2 ! · 0·4 ! ! 4 0·02 ! ! 4 0·8 !

b 0·348 ! 4 0·06 ! ! 4 0·2 ! ! 4 0·4 !

c 0·485 ! 4 0·05 ! ! · 0·6 ! ! 4 0·3 !

TASK 9.4

M�1 Which of the numbers below are correctly rounded off:

a 48 ! 50 (to nearest 10) b 152 ! 100 (to nearest 100)

c 124 ! 130 (to nearest 10) d 3817 ! 4000 (to nearest 1000)

e 6·2 ! 6 (to nearest whole number) f 42 ! 40 (to nearest 10)

g 5·9 ! 5 (to nearest whole number) h 9500 ! 9000 (to nearest 1000)

i 4750 ! 4800 (to nearest 100) j 8·49 ! 9 (to nearest whole number)

�2 Which of these numbers will round to 7000 when rounded to the nearest 1000:

7604 6450 6550 6508 6878 6243 6500 7143 7500 7338

�3 10 800 people live in the city of Wells (to the nearest 100). Write down

the least number of people that might live in Wells.

�4 Round each of these numbers to the nearest whole number:

a 7·6 b 14·5 c 0·82 d 52·17 e 14·48

�5 75 000 people went on a protest march. If this number had been

rounded to the nearest 1000, write down the lowest number of people

that might have been on the protest march.

E�1 Round each of these numbers to the nearest 1 kg:

a 2·9 kg b 4·28 kg c 8·47 kg d 3·814 kg e 15·613 kg

61

�2 8·5238176 is 9 to the nearest whole number because the first

digit after the decimal point is 5 or more so round up.

Round each of these numbers to the nearest whole number:

a 3·498173 b 6·281365

c 12·817624 d 38·48932

e 0·724816 f 67·5186326

�3 Work out these answers on a calculator and then round off the answer to the nearest

whole number. Which answer is the odd one out?

a 431 4 28 b 48·3 · 0·3206 c 3·91782 d 624 4 37

�4 58 · 81 is roughly 60 · 80 = 4800.

Work out a rough answer to each Question below by rounding each number

to the nearest 10:

a 89 4 32 b 42 · 91 c 78 4 11 d 592

e 99 · 98 f 359 2 72 g 193 h 349 4 68

TASK 9.5

M�1 Which of the numbers below are correctly rounded off to the number

of decimal places shown:

a 3·68 ! 3·6 (to 1 decimal place) b 5·74 ! 5·7 (to 1 decimal place)

c 5·53 ! 5·5 (to 1 decimal place) d 8·264 ! 8·27 (to 2 decimal places)

e 6·828 ! 6·83 (to 2 decimal places) f 17·614 ! 17·6 (to 1 decimal place)

�2 Round these numbers to 2 decimal places.

a 4·814 b 0·363 c 28·1894 d 5·645

�3 Which numbers opposite

round to 6·74 (to

2 decimal places)?

6·74 6·73512

6·7426·746

6·7534

6·738 6·749

�4 Work out these answers on a calculator and then round the answers to

the accuracy shown.

a 4·16 · 2·7 (to 1 decimal place) b 14·6 4 7 (to 2 decimal places)

c 284 4 31 (to 1 decimal place) d 0·3872 (to 2 decimal places)

e 9 4 0·53 (to 3 decimal places) fffiffiffiffiffi29p

(to 2 decimal places)

g (7·16 2 3·49)2 (to 3 decimal places) h 0·72 · 0·81 · 0·3 (to 3 decimal places)

62

E�1 5·3 · 7·8 = 41·34. Is this likely to be correct?

5·3 · 7·8 is roughly 5 · 8 = 40 so the answer 41·34 is likely to be correct.

Write down which answers below are likely to be correct by finding

sensible rough answers. Do not use a calculator.

a 4·8 · 88 = 422·4 b 7·9 · 12·85 = 1015·15

c 58·16 2 17·96 = 40·2 d 8·042 = 646·416

e 19·9 · 30·14 = 59·9786 f 2·063 = 874·1816

�2 Estimate the area of this rectangle. 14·98 cm3·07 cm

�3 A shop sells 47 selection boxes for Christmas. Each selection box costs £3·89.

Estimate how much money the shop receives for the selection boxes.

�4 A rectangular room measures 6·2 m by 4·84 m. Carpet costs £19·95

per square metre. Estimate how much it will cost to carpet the room.

�5 Do not use a calculator.

Use sensible rough answers to match each Question below to the correct answer:

3·12 × 12·89

13·08 − 2·97

16·11 × 6·019

349 ÷ 50

6·892

A

B

C

D

E

47·4721

6·98

40·2168

10·11

96·96609

P

Q

R

S

T

TASK 9.6

M

Use a calculator.�1 Work out

a 29 4 (23) b 25·6 · 24·7 c 28·1 · 217

d (2·8 + 3·4) · 0·9 e 4·6 · (6·2 2 3·7) f 2·632

63

�2 Work out the following and give your answer in pounds.

a £4·15 · 4 b £3·80 · 9 c £230·52 4 17

d 160 · 3p e £7·60 · 12 f 14p · 270

�3 Each of the calculations below is wrong.

Find the correct answer for each calculation.

a 48 + 32

20= 49·6 b 51 2 31

10= 47·9

c 50

25 · 10= 20 d 75

40 2 20= 218·125

�4 Work out the following, giving answers to the nearest whole number.

Match each calculation to the correct answer.

16 + 4·9 − 3·17

3·4 × (5·8 − 4·25)

8·7 + 2·41·6

35·2(4·9 − 0·18)

24·632·17 + 3·42

13·8 + 9·162·4 × 3·7

7

4

18

5

10

3

P

Q

R

S

T

U

A

B

C

D

E

F

E�1 Write down the fractions shown on the calculator displays below:

a b c

�2 Use a calculator to work out

a 4

52

2

3b 4

94

1

3c 11

5· 32

7d 41

2415

6

�3 Work out

a 3·42 bffiffiffiffiffiffiffiffiffi0·49p

cffiffiffiffiffiffiffiffiffiffiffi13·69p

d (7 + 9)2

e 83 fffiffiffiffiffiffiffiffiffiffiffi38·44p

g 45 hffiffiffiffiffiffiffiffi7293p

64

�4 27 minutes = 27

60of an hour = 27 4 60 = 0·45 hours. Write these

time intervals in hours as decimals.

a 24 minutes b 33 minutes c 57 minutes

d 3 hours 15 minutes e 2 hours 6 minutes f 5 hours 42 minutes

�5 Work out and give each answer correct to 2 decimal places.

a 17·46

ð4·17 + 0·8Þ b 8·623 + 4·92 c 2·62 · (9·8321·64)

d 13·6 + 19·5

2·74e 34·16

3·6 · 1·7f 17·2 + 8·16

8·6122·48

TASK 9.7

M�1 Write the numbers below correct to 3 significant figures.

a 3·168 b 5·6163 c 41·689 d 0·1472

e 16·594 f 61 749 g 26 447 h 317·58

�2 Which numbers below round to 37 200 (to 3 significant figures)?

37 200

37 261 37 169

37 212

37 13437 149

37 241

�3 Which numbers below are correctly rounded off to 2 significant

figures?

a 5·65 = 5·7 b 4189 = 4100

c 0·0176 = 0·018 d 0·0607 = 0·061

�4 Use a calculator to work out the following, giving each answer to the number

of significant figures shown.

a 64 4 3.7 (3 s.f.) b 20·8 · 11·6 (2 s.f.)

c (8·14 + 6·5) · 19 (2 s.f.) d 14·62 (3 s.f.)

e 48 2 12·61 (3 s.f.) f 172 · 486 (2 s.f.)

g 13·63 4 0·18 (1 s.f.) h 4·8

(6·4 + 2·34)(2 s.f.)

65

E�1 Estimate, correct to 1 significant figure:

a 6·9 · 10·01 b 28·03 4 6·89 c 19·932 d 4·9 + 15·12

1·961e 9·042 + 18·87

20·07

f 1

8of £23 998 g 3

4of £79 999 h 26% of £12 134 i 29·892 + 19·9

19·94 2 10·103

�2 Do not use a calculator.

384 · 27 = 10 368

Work out

a 10 368 4 27 b 10 368 4 384 c 38·4 · 27

�3 Do not use a calculator.

486 · 147 = 71 442

Work out

a 71 442 4 147 b 48·6 · 14·7 c 4·86 · 14·7

�4 Do not use a calculator.

37 107 4 63 = 589

Work out

a 589 · 63 b 37 107 4 589 c 3710·7 4 6·3

ALGEBRA 2 10

TASK 10.1

�1 a Copy this grid.

0 1 2 3−3 −2 x

y

1

2

3

−1

−2

−3

−1

b Draw the line y = 3.

c Draw the line y = 22.

d Draw the line x = 1.

e Write down the co-ordinates

where the line x = 1 meets the

line y = 22.

66

�2 a Write down the equation of the

line which passes through P and R.

0 1 2 3−3 −2 x

y

1

2

3

−1

−2

−3

T

P

S

R

U

VQW

−1

b Write down the equation of the line

which passes through S and U.

c Write down the equation of the line

which passes through P and Q.

d Write down the equation of the line

which passes through W, Q and V.

E

For Questions�1 and�2 , you will need to draw axes like these:�1 Copy and complete the table below then draw the

straight line y = 2x + 1.

00 1 2 3 4

12345678

x

y

x 0 1 2 3

y 5

�2 Copy and complete the table below then draw the

straight line y = 4 2 x.

x 0 1 2 3

y

�3 Using x-values from 0 to 4, complete a table then draw the

straight line y = 4x (make sure you draw the axes big enough).

For Questions�4 and�5 , you will need to draw axes likethese:�4 Copy and complete the table below

then draw the straight line y = 2x 2 4.

x 21 0 1 2 3

y

�5 Copy and complete the table below then draw the

straight line y = 3x + 1.

x 22 21 0 1

y

0 1 2 3−3 −2 x

y

12345

−1−2−3−4−5−6

−1

67

�6 Using x-values from 23 to 3, complete a table then draw the straight line

y = 2x + 3 (make sure you draw the axes big enough).

TASK 10.2

M�1 Find the value of these when x = 23:

a x2 b x2 + 2 c x2 2 4 d x2 + 2x e x2 2 x

For Questions�2 and�3 , you will need to draw axes like these:�2 Complete the table below then draw the

curve y = x2 + 2.

x 23 22 21 0 1 2 3

y

�3 Complete the table below then draw the

curve y = x2 2 1.

0 321−2−3 x

y

123456789

1011

−1−1

x 23 22 21 0 1 2 3

y

�4 a Complete the table below for y = 4x2

(4x2 means x2 then ‘multiply by 4’).

x 22 21 0 1 2

y

b Draw an x-axis from 23 to 3 (use 2 cm for 1 unit) and a y-axis

from 0 to 18 (use 1 cm for 2 units). Draw the curve y = 4x2.

E

For Questions�1 and�2 , you will need to draw axes like those shown on the

next page.�1 Complete the table below then draw the curve y = x2 + 3x.

x 23 22 21 0 1 2 3

x2 1 4

+3x 23 6

y 22 10

68

�2 Complete the table below then draw

the curve y = x2 + 2x 2 5.

0 321−2−3 x

y

2468

1012141618

−2−4−6

−1

x 23 22 21 0 1 2 3

x2 9

+ 2x 26

25 25

y 22

�3 Complete the table below then draw y = x3 + 2x.

x 23 22 21 0 1 2 3

x3

+ 2x

y

TASK 10.3

M�1 a Draw these axes.

0 1 2 3 4 5 60

2

1

3

4

5

6

x

yb If 3x + y = 6, find the value of

y when x = 0.

c If 3x + y = 6, find the value of

x when y = 0.

d Plot 2 points from b and c and join them up to

make the straight line 3x + y = 6.

�2 a Draw the same axes as in Question�1 .b Use x = 0 then y = 0 to find

2 points for 2x + 3y = 12.

c Draw the straight line 2x + 3y = 12.

�3 a Draw an x-axis from x = 0 to 8 and a

y-axis from y = 0 to 5.

b Use the cover-up method with x = 0 and

y = 0 to draw 3x + 7y = 21.

�4 a Draw an x-axis from x = 0 to 6 and a y-axis from y = 0 to 10.

b Use the cover-up method with x = 0 and y = 0 to draw 8x + 5y = 40.

69

E

0 1 2 3 4 5 60

2

1

3

4

5

6

7

x

y

x + y = 6

2x −

y =

6

x − 2y = −6

�1 Use the graph to solve the simultaneous

equations below:

a x + y = 6

2x 2 y = 6

b x 2 2y = 26

2x 2 y = 6

c x + y = 6

x 2 2y = 26

�2 a Draw an x-axis from 0 to 7.

Draw a y-axis from 25 to 5.

b Use the cover-up method to draw the line 2x + 3y = 12.

c Use the cover-up method to draw the line 4x 2 2y = 8.

d Use your graph to solve the simultaneous equations

2x + 3y = 12

4x 2 2y = 8

�3 a Draw x and y axes from 22 to 5.

b Draw the lines x + y = 4 and y = x + 2.

c Solve graphically the simultaneous equations

x + y = 4

y = x + 2

TASK 10.4

M

Find the gradient of each line.

�1

0 1 2 3 4 5 60

2

1

3

4

5

6

x

y

2

4

�2

0 1 2 3 4 5 60

2

1

3

4

5

6

x

yRemember:

Gradient =vertical distance

horizontal distance

70

�3

A

B

C D E0 1 2 3 4 5 6 7 8 9

0

2

1

3

4

5

6

7

8

9

x

y

�4 Draw a graph to help you if you need to.

Find the gradient of the line joining the points:

a (1, 1) and (3, 5) b (2, 4) and (3, 7)

c (3, 1) and (5, 4) d (1, 0) and (4, 5)

E�1 Find the gradient of each line below:Remember: a

line sloping

downwards to

the right has a

negative gradient

A B C D

E

F

0 1 2 3 4 5 6 7 8 9 10 11 120

2

1

3

4

5

6

7

8

9

10

x

y

71

�2 Find the gradient of the line joining each pair of points below

(draw a graph to help if you need to):

a (3, 6) and (5, 2) b (1, 4) and (3, 2)

c (0, 5) and (2, 4) d (1, 5) and (5, 2)

�3 Find the gradient of each line below (look at the numbers on the

axes very carefully):

a b

�4 Which of the following lines are parallel:

y = x + 4, y = 4x + 1, y = 4 2 3x,

y = 5 + 4x, y = 2x + 4

�5 Write down the gradient of these lines

a y = 3x + 2 b y = 8x 2 4 c y = 1

3x 2 2

d y = 5 2 4x e y = 9 + x

TASK 10.5

M�1 A crowd of 8000 people attended a football match which started at 3 p.m.

The graph below shows the number of people who had entered the

ground at different times.

1000012 noon

Number of people in the ground

Time1 p.m. 2 p.m. 3 p.m.

2000300040005000600070008000

1

20

00 1 2 3 4 5

10

20

30

40

x

y

00 1 2 3 4 5

5

10

15

20

x

y

72

How many people had entered the ground by the following times?

a 1 p.m. b 1:15 p.m. c 2:15 p.m. d 12:45 p.m.

e During which half-hour interval did the least number of people

enter the ground?

�2 The graph opposite shows the temperature

during a day:

a What was the temperature at 1 p.m.?

012 noon 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m.

Time

6 p.m.

10

20

30

40

x

y

Tem

pera

ture

(°C

)

b What was the temperature at

4.30 p.m.?

c At what time was the temperature

20 �C?

d When was the temperature 15 �C?

e When did the temperature start

falling?

f How much did it fall by?

E�1

00800 0900 1000 1100

20

40

60

80

100Swindon

Bristol

Distance fromAxbridge (km)

Time

Axbridge

The graph shows the journey of a car from Axbridge to Swindon

via Bristol. The vertical axis shows the distance of the car from

Axbridge between 0800 and 1100.

a How far was the car from Axbridge at 0815?

b For how long did the car stop at Bristol?

c Find the speed of the car (in km/h) between Axbridge and Bristol.

d Find the speed of the car (in km/h) between Bristol and Swindon.

73

�2 The graph opposite shows a car

journey from Manchester.

00800 0900 1000 1100

20

40

60

80

100

120

Distance fromManchester (km)

Time

A

B C

DE

a How far from Manchester is the

car at 1030?

b When is the car half way between

B and C?

c At what time is the car 30 km from

Manchester?

d Find the speed (in km/h) of the car

from B to C.

e Find the speed (in km/h) of the car

from C to D.

�3 Copy these axes and sketch the graph

of a car travelling at a steady speed

then accelerating rapidly. distance

time

DATA 1 11

TASK 11.1

M�1 For each statement below, write down whether it is:

impossible unlikely even chance likely certain

a It will snow in January.

b The next baby born will be a girl.

c You will go to the toilet within the next week.

d A friend will give you £10 000 within the next hour.

e You will get ‘heads’ if you toss a coin.

74

�2 a Copy this probability scale.

impossible even chance certainlikelyunlikely

0 1

Use an arrow to place each event below on your probability scale:

b You get a 5 if you roll a dice.

c It will be the weekend within the next 7 days.

d You will get a red card if you take one card from a pack of playing

cards (26 cards out of 52 are red in a full pack).

e You will wake up in Mexico tomorrow morning.

f You will eat during the next 24 hours.

E�1 Sandeep throws a dice 180 times. The dice lands 72 times

on a ‘2’.

a How many times should the dice land on a ‘2’ if the dice

is fair?

b From Sandeep’s results, find the relative frequency of getting

a ‘2’.

�relative frequency =

number of times event happens

total number of trials

�

c Do you think the dice is fair? Explain the answer you give.

�2 Freddie throws a coin 120 times. The coin lands on ‘tails’

58 times.

a From Freddie’s results, find the relative frequency of getting

‘tails’.

b Do you think the coin is fair? Explain the answer you give.

�3 Jo is throwing an 8-sided dice. She throws the dice 240 times.

The table below shows her results.

Score 1 2 3 4 5 6 7 8

Frequency 27 24 36 27 30 27 33 36

a How many times should each number come up if the dice

is fair?

b From Jo’s results, use a calculator to find the relative

frequency of getting each score (1 up to 8).

c Do you think the dice is fair? Explain the answer you give.

75

TASK 11.2

M�1 Sue has 15 cards as shown below:

T E L E V I S I O N C A L L S

Sue picks a card at random.

What is the probability that she picks the letter:

a C b E c L d S

�2 Angus has a bag which contains 7 toffees, 4 mints and 2 chocolates.

Angus picks one of these sweets.

What is the probability that he chooses a:

a mint b mint or toffee c mint or chocolate

�3 A bag contains 10 beads. There are 6 blue,

3 red and 1 green.

BB

BB B

B G

RR

Ra Find the probability of selecting a red bead.

b 2 more blue beads are put in the bag. Find

the probability of selecting a blue bead.

�4 24 people come for a job interview. 9 of these people wear glasses and

4 of them have contact lenses.

Find the probability that the person chosen for the job:

a has contact lenses

b wears glasses

c does not wear glasses or contact lenses

�5 Wendy has six £5 notes, ten £10 notes and four £20 notes in her purse.

If she takes out one note, what is the probability that it will be:

a a £20 note b a £5 or £10 note c a £50 note

d She buys a new toaster with a £20 note and a £10 note. If she

now took out a note, what is the probability that it would be a

£10 note?

E�1 A coin is thrown 48 times. How many times would you expect

it to land on ‘heads’?

�2 A dice is thrown 120 times.

How many times would you expect to get a:

a 3 b 5 c 4 or 5 d square number

76

�3 This spinner is spun 80 times. How many

times should the spinner land on a ‘0’?

0

0

0 0

1�4 The probability of Canning Albion winning a football match

is 2

3. If they play 42 matches in a season, how many matches are

they likely to win?

�5 The probability of Rob going to the pub on any one day is 2

7.

How many times is he likely to go to the pub in the next fortnight?

�6 A bag contains 5 blue balls, 4 red balls

and 1 yellow ball.

Brenda takes out one ball at random and

then puts it back. If she does this 70 times,

how many times would she take out: BB BBB

RR R

R Ya a yellow ball

b a blue ball

c a blue or red ball

�7 A bag has only red and blue discs in it. The probability of picking

red is 2

5.

a What is the probability of picking a blue disc?

b Sam picks out 4 red discs without replacing them. What is the

smallest number of blue discs that could have been in the bag?

c If Sam picks out a total of 5 red discs without replacing them,

what is the smallest number of blue discs that could have

been in the bag?

TASK 11.3

M�1 At a cafe, each person has a main course and a pudding.

One lunchtime the menu is:

main course: Cottage pie or Macaroni cheese

pudding: Trifle or Apple pie

List all the different meals that could be ordered.

77

�2 Here are 2 spinners. If I spin both spinners,

I could get a ‘1’ and a ‘4’ (1, 4).

1

278

2 9

4 12

a List all the possible outcomes.

b How many possible outcomes are there?

�3 Three babies are born. List all the boy/girl mixes

(example: B G B boy, girl, boy).

�4 Bart has 4 films (Antz, King Kong, Jungle Book and The Terminator).

He only has time to watch two of the films. List all the possible

pairs of films that he could watch.

�5 Nina has 2 spinners. She spins both spinners

and multiplies the numbers.

For example a ‘3’ and a ‘4’ give 12.

2 3

1 4

2 3

1 4a Copy and complete this grid to show all the

possible outcomes.

× 1

1

2

2

3

3 12

4

4

b Find the probability of getting an answer

of 4 when the 2 numbers are multiplied

together.

E�1 The probability of a bus being late is 0·2. What is the probability of the bus

not being late?

�2 The probability of Sean getting up before 11 a.m. on a Saturday morning is 1

4.

What is the probability of Sean not getting up before 11 a.m. on

a Saturday morning?

�3 The probability of Karen playing certain sports is shown in the

table below.

hockey football badminton netball

0·5 0·1 x 0·2

a What is the probability of Karen playing hockey or netball?

b What is the probability of Karen playing badminton?

78

�4 The probability of picking a picture card from a pack of cards is 3

13.

What is the probability of not picking a picture card?

�5 If the probability of England winning the next football World Cup is

0·15, what is the probability of England not winning the

next World Cup?

�6 Don gets to work by either car, bus, tube or bike. The table

shows the probability of each being used.

car bus tube bike

0·25 0·4 0·2

a What is the probability of Don going to work by bus.

b What is the probability of Don going to work by car or bus.

c On his 20 working days in March, how many days would

you expect Don to take the tube?

ALGEBRA 3 12

TASK 12.1

M

In Questions�1 to�8 copy the sequences and write the next 2 numbers.

What is the rule for each sequence?�1 5, 8, 11, 14, ... �2 8, 20, 32, 44, ...�3 44, 39, 34, 29, ... �4 3, 4, 6, 9, ...�5 61, 52, 43, 34, ... �6 10, 15, 25, 40, ...�7 11, 5, 21, 27, ... �8 14, 8, 2, 24, ...

�9 You are given the first term of a sequence and the rule. Write down

the first 5 terms of each sequence.

a First term = 7 Rule: add 8

b First term = 61 Rule: subtract 7

c First term = 19 Rule: subtract 5

In Questions�10 to�13 write down the missing numbers.

�10 22, 19, , 13, �11 5, 12, , 26,

�12 29, 25, , , 7 �13 , 20, 14, 8,

79

�14 How many dots are needed for

a shape 4

b shape 5

Shape 1 Shape 2 Shape 3

�15 How many squares are

needed for

a shape 5

b shape 6

Shape 1 Shape 2 Shape 3 Shape 4

E

In Questions�1 to�6 copy the sequences and write the next 2 numbers.�1 3, 6, 12, 24, ... �2 80, 40, 20, 10, ...�3 4, 12, 36, 108, ... �4 4·9, 4·1, 3·3, 2·5, ...�5 3000, 300, 30, 3, ... �6 21, 22, 24, 28, ...

�7 The first four terms of a sequence are 2, 8, 14, 20.

The 50th. term in the sequence is 296.

Write down the 49th. term.

�8 Shape 1 Shape 2 Shape 3 Shape 4

How many small

squares are needed for

a shape 5

b shape 6

80

In Questions�9 to�12 find the next 2 numbers in each sequence (it may help you

to work out the 2nd. differences).�9 2, 5, 10, 17, ... �10 0, 3, 8, 15, ...�11 2, 6, 12, 20, ... �12 2, 8, 16, 26, ...

�13 The first five terms of a sequence are 1, 2, 4, 8, 16, ...

The 9th. term in the sequence is 512.

Write down the 10th. term of the sequence.

�14 Find the next 2 numbers in the sequence below.

Try to explain the pattern.

0, 1, 3, 7, 15, ...

TASK 12.2

M�1 Write down the term-to-term rule for each sequence below:

a 3, 12, 48, 192, ... b 53, 45, 37, 29, ...

c 9, 6·5, 4, 1·5, ... d 2, 5, 14, 41, 122, ...

�2 The nth. term of a sequence is given by the formula nth. term = 2n + 1.

Use values of n from 1 to 5 to write down the first 5 terms of the

sequence.

�3 Use each nth. term formula below to find the first 5 terms of each

sequence.

a nth. term = 3n + 5 b nth. term = 4n 2 1 c nth. term = 2n + 7

�4 Here is a sequence: 5, 8, 11, 14, ...

The 1st. difference is +3.

Copy and complete the table which has

a row for ‘3n’.

Copy and complete: ‘The nth. term of the

sequence is 3n + ’

Position n 1 2 3 4

term 5 8 11 14

3n 3 12

�5 Use the tables below to help you find the nth. term of each

sequence.

a Sequence 2, 7, 12, 17, ... b Sequence 7, 11, 15, 19, ...

Position n 1 2 3 4

term 2 7 12 17

5n 5 10 15 20

Position n 1 2 3 4

term 7 11 15 19

4n 4 8 12 16

nth. term = nth. term =

81

�6 Match up each sequence to the correct nth. term formula.

6, 8, 10, 12, ...

3, 8, 13, 18, ...

11, 16, 21, 26, ...

8, 10, 12, 14, ...

nth. term = 2n + 6

nth. term = 5n − 2

nth. term = 2n + 4

nth. term = 5n + 6

P

Q

R

S

A

B

C

D

�7 Find the nth. term of each sequence below (make a table like Question�5if you need to).

a 7, 10, 13, 16, ... b 9, 16, 23, 30, ...

c 1, 10, 19, 26, ... d 6, 14, 22, 30, ...

e 30, 26, 22, 18, ... f 18, 13, 8, 3, ...

g 8, 12, 16, 20, ... h 22, 19, 16, 13, ...

E�1 Here is a sequence of shapes made from squares.

Let n = shape number and w = number of white squares.

n = 1w = 10

n = 2w = 12

n = 3w = 14

a Draw the next shape in the sequence.

b How many white squares are in shape number 4?

c Copy and complete the table of values.

The 1st. difference is +2.n 1 2 3 4

w 10 12 14

d Find a formula for the number of white squares (w) for the

shape number n. Use values of n to check if your formula

is correct.

e Use your formula to find out how many white squares are in

shape number 50.

82

�2n = 1s = 8

n = 2s = 15 s =

n = 3

a Draw the next shape in the sequence.

b Let n = shape number and s = number of sticks.

Complete a table of values for n and s.

c Use the table and 1st. difference to find a formula for the number of sticks (s)

for the shape number n.

Use values of n to check if each formula is correct.

d Use the formula to find out how many sticks are in shape number 40.

�3 Repeat Question�2 for the sequence below:

n = 1

n = 2n = 3

TASK 12.3

M�1 Solve these equations:

a n + 3 = 8 b n + 8 = 15 c n 2 3 = 6 d n 2 7 = 9

e n + 12 = 43 f x 2 9 = 19 g x 2 24 = 18 h x + 37 = 60

i x + 26 = 41 j x 2 38 = 14 k n 2 49 = 28 l n + 58 = 73�2 Ian thinks of a number and then subtracts 14. If the answer is 25,

what number did Ian think of ?�3 Solve

a 6 · n = 30 b 6n = 24 c 3n = 21 d n 2 14 = 21

e n 4 3 = 5 f n

4= 2 g x

10= 6 h x

7= 4

i x

5= 8 j 8x = 48 k x 2 34 = 28 l 9x = 54

�4 Find the value of x in this rectangle.16

8

x − 2

8

83

E�1 Solve these equations:

a n + 3 = 1 b n + 2 = 1 c n + 5 = 3 d n 2 3 = 26

e n + 8 = 0 f 3n = 26 g 10x = 28 h 25x = 220

i 4n = 228 j n 4 3 = 24 k x

5= 25 l x

7= 23

�2 Pat thinks of a number and then adds 10. If the answer is 5,

what number did Pat think of ?

�3 Teresa doubles a number and gets the answer 9.

What was the number?

�4 Solve Remember:

if 3x = 2 then

x = 2

3

a 2x = 1 b 2x = 5 c 3n = 7 d 5n = 4

e 2n = 23 f 5x = 7 g 7x = 24 h 3n = 211

TASK 12.4

M

In Questions�1 to�3 , copy and fill the empty boxes.

�1 3n + 2 = 20 �2 5n + 6 = 26 �3 4x 2 7 = 1

3n = 18 5n = 4x =

n = n = x =

Solve these equations:

�4 2n + 1 = 9 �5 3n + 8 = 17 �6 6n + 4 = 16�7 3n + 5 = 20 �8 4x + 6 = 18 �9 5x 2 2 = 18�10 8x 2 1 = 23 �11 6x 2 7 = 23 �12 3n 2 8 = 19

�13 Find the value of x in this rectangle. 19

6

4x − 9

6

Solve:�14 8x + 2 = 50 �15 9x 2 8 = 55 �16 6n 2 10 = 32�17 6n + 8 = 62 �18 7x 2 14 = 35 �19 39 = 3x + 9�20 34 = 5x 2 6 �21 8n 2 26 = 30 �22 29 = 9x 2 7

84

E

In Questions�1 to�3 , copy and fill the empty boxes.�1 3n + 4 = 6 �2 5n + 6 = 9 �3 10 = 18 + 2n

3n = 2 5n = = 2n

n = 2

n = = n

Solve these equations:�4 5n + 4 = 7 �5 2x + 5 = 10 �6 4x + 7 = 10�7 8x + 5 = 10 �8 3n + 6 = 13 �9 2n 2 9 = 2�10 4n 2 2 = 1 �11 9x 2 5 = 2 �12 10x + 14 = 37�13 If we multiply a number by 5 and then add 3, the answer is 4. What

is the number?

�14 If we multiply a number by 7 and then subtract 2, the answer is 3.

What is the number?

Solve:�15 3n + 8 = 6 �16 5n + 6 = 4 �17 6x + 7 = 6�18 8 = 20 + 4x �19 15 = 27 + 3x �20 8x 2 2 = 25

TASK 12.5

M

In Questions�1 to�3 , copy and fill the empty boxes.�1 4(n + 2) = 20 �2 3(2n + 3) = 15 �3 2(2n23) = 14

4n + 8 = 20 6n + = 15 2 6 = 14

4n = 6n = = 20

n = n = n =

Solve these equations:�4 3(n + 1) = 15 �5 5(n + 4) = 30 �6 10(n 2 4) = 70�7 4(n 2 3) = 24 �8 6(x 2 5) = 18 �9 2(2x + 3) = 14�10 5(2x 2 1) = 25 �11 3(2n + 7) = 27 �12 6(n 2 4) = 36�13 I think of a number. I add 9 onto the number then multiply the answer

by 3. This gives 36. What was the number I started with?

Solve:�14 2(2x 2 4) = 12 �15 4(2n + 5) = 52 �16 2(3n 2 5) = 20�17 3(3x + 6) = 54 �18 5(2n 2 6) = 40 �19 4(2x 2 7) = 20

85

E

In Questions�1 to�3 , copy and fill the empty boxes.�1 2(n + 5) = 11 �2 3(2n + 3) = 3 �3 5(x + 2) = 8

+ 10 = 11 6n + = 3 5x + = 8

= 1 6n = 5x =

n = n = x =

Solve these equations:�4 2(n + 3) = 3 �5 5(x + 2) = 6 �6 3(2x 2 1) = 2�7 5(2x + 3) = 18 �8 4(n 2 2) = 11 �9 6 = 3(n + 4)�10 18 = 2(6 2 x) �11 70 = 10(2 2 5x) �12 3(2n + 5) = 14

TASK 12.6

M

Find the value of n in Questions�1 to�4 :�1 n n 1 n 8 �2 n nn n n 4 n n n 10

�3 n n nn n n n 2 n n n n 17

�4 n nn n n n 11

nn n n 19

Solve these equations:�5 5n + 9 = 4n + 18 �6 8n + 7 = 3n + 2�7 7x + 6 = 3x + 18 �8 9x + 1 = 2x + 43

In Questions�9 and�10 , copy and fill the empty boxes.�9 6n23 = 2n + 17 �10 8x 2 9 = 3x + 26

4n23 = 17 2 9 = 26

4n = 20 = 35

n = x =

Solve these equations:�11 5n 2 3 = 2n + 18 �12 8n 2 3 = 2n + 27�13 4n 2 9 = 3n + 7 �14 9x 2 6 = 6x + 18�15 6x + 12 = 2x + 20 �16 8x 2 10 = 5x + 20�17 5x 2 7 = x + 29 �18 4n + 13 = 2n + 25�19 7n 2 8 = 3n + 28 �20 10x 2 6 = 7x + 15

86

E

In Questions�1 to�3 , copy and fill the empty boxes.�1 5x + 12 = 2x + 10

3x + 12 = 10

3x =

x =

�2 3(2x + 4) = 4(x + 6)

6x + = + 24

2x =

x =

�3 5n 2 2 = 3n 2 8

2n 2 2 = 28

2n =

n =

Solve these equations:�4 4x + 3 = x + 4 �5 7n + 4 = 2n + 8 �6 5n + 3 = 27 2 n�7 3x + 9 = 44 2 2x �8 6x + 10 = 4x + 6 �9 5x + 19 = 11 2 3x

�10 This is an isosceles triangle.

Find the value of x.4x − 8 2x + 12

Solve:�11 4(2x + 1) = 2(3x + 5) �12 5(3x + 4) = 4(3x + 20)�13 2(4x 2 3) = 5(x + 6) �14 4(3n 2 1) = 2(5n + 7)�15 5(2n + 4) = 2(4n + 3) �16 3(3x + 2) + 5(x + 4) = 54

TASK 12.7

M

Solve these equations:�1 3x + 7 = 31 �2 x

3+ 7 = 10 �3 x

4+ 9 = 15

�4 x

8� 5 = 1 �5 5x 2 10 = 30 �6 x

5� 2 = 8

�7 a Write down an equation using the angles.

2x

3x

x

b Find x.

c Write down the actual value of each angle in this triangle.

�8 The area of this rectangle is 60 cm2.

(3x + 2) cm

3 cma Write down an equation involving x.

b Find x.

87

�9 The perimeter of the rectangle opposite is 50 cm.

x cm

(x + 7) cma Write down an equation using the perimeter.

b Find x.

c Write down the actual length and width of the rectangle.

Solve these equations:�10 x

7� 4 = 4 �11 x� 4

7= 4 �12 x + 9

4= 6

�13 4(2x + 1) = 28 �14 x

5� 3 = 2 �15 x 2 8

6= 5

E

Solve these equations:�1 5(2x 2 3) = 3(x + 2) �2 x + 7

6= 3

�3 x

4+ 6 = 3 �4 5n + 10 = 3n + 2

�5 2(4n 2 1) = 3(2n + 5) �6 3x + 5

2= 3

�7 30

x= 5 �8 8 = 56

x

�9 2n + 16

5= 2 �10 7 2 2x = 3x + 3

�11 a Write down an equation using

the angles.Remember:

the angles in a

quadrilateral

add up to 360�.

b Find x.

5x + 70

7x + 30

5x + 60

3x + 60

c Write down the actual value of each

angle in this quadrilateral.

�12 The length of a rectangle is 8 cm more than its width. If its perimeter is 44 cm,

find its width.

�13 Hannah has 3 times as much money as Joe. Hannah spends £24 on a new blouse.

She now has £30 left. How much money has Joe got?

�14 This is an isosceles triangle. 3x + 2

2x + 1

7x − 14

a Find the value of x.

b Find the perimeter of the triangle.

88

�15 The areas of each rectangle are equal

(all lengths are measured in cm).3

4x − 35

2x + 3

a Find the value of x.

b Find the area of one of the rectangles.

TASK 12.8

M�1 The area of this rectangle is 25 cm2.

7 cm

x cmCopy and complete this table to find x to 1 decimal place.

trial calculation too large or too small?

x = 3 7 · 3 = ... too small

x = 4 7 · 4 = ... too large

x = 3·5 7 · 3·5 = ... too ...

x = 3·6 7 · 3·6 = ... too ...

So x = ... to 1 decimal place.

�2 The area of this square is 85 cm2.

x cm

x cm

Area = x · x = x2

We want x2 = 85

Copy and complete this table to find x to 1 decimal place.

trial calculation too large or too small?

x = 10 10 · 10 = 100 too large

x = 9 9 · 9 = ... too ...

x = 9·5 9·5 · 9·5 = ... too ...

x = 9·2 9·2 · 9·2 = ... too ...

x = 9·3 9·3 · 9·3 = ... too ...

So x = ... to 1 decimal place.

89

�3 The volume of this cube is 250 cm3.

Use trial and improvement to find x to 1 decimal place.

x cm

x cmx cm

E�1 The area of this rectangle is 42 cm2. Use trial and

improvement to find x to 2 decimal places.

Show all your working out.x cm

(x + 4) cm

�2 Solve these equations by trial and improvement. Give each answer

to 2 decimal places. Show all your working out.

a x2 2 3x = 15 b x3 + x = 788 c x3 2 5x = 267

DATA 2 13

TASK 13.1

M�1 Write the following numbers in order of size then write down

the median.

7 2 18 4 6 14 12 19 14

�2 Find the mode of each set of numbers below:

a 3 7 1 4 5 3 5 2 3 4 9 3 6

b 5 4 6 2 4 6 1 6 2 8 3 2

�3 There are 5 people aged

23, 48, 46, 9 and 58 in a Rolls Royce.

There are 4 people aged

57, 28, 4 and 31 in a Citroen Saxo.

Which car contains the larger range of ages?

90

�4 10 people weigh the following (in kg):

65 85 70 65 80 95 70 85 90 95

Find their mean average weight.

For each set of numbers below, find

a the mean

b the median

c the mode and

d the range.

�5 6 10 9 3 16 10 2

�6 8 11 4 8 15 4 16 5 10

�7 6 3 9 9 2 7

�8 The number of children in each of 20 families is shown below:

2 3 0 1 4

1 2 1 2 0

3 2 2 1 5

2 1 2 0 2

Use a calculator to work out the mean average number of children

in each family.

�9 The ages of the members of a football team are:

19 27 22 21 24 33 29 26 22 18 31

Two players are ‘sent off ’ in a match. They are the 29 year-old

and the 18 year-old.

Find the mean age of the players left on the pitch.

E�1 Seven people score the following marks in a test:

30 40 40 40 45 45 96

Find a the mean

b the median

c Which average best describes these marks? Explain why.

�2 In a shooting match, Rose scores:

8, 9, 9, 9, 10, 9, 9, 9, 9, 10

Find a the mode

b the mean

c Which average best describes these scores, the mode or

the mean? Explain why.

�3 4 9

Ross has 5 cards.

The 5 cards have a mean of 7, a median of 7 and a range of 13.

What are the 5 numbers on the cards?

91

�4 The mean average age of 6 people is 37.

What is the total of all their ages?

�5 The mean weight of 11 people is 63 kg.

a What is the total weight of all 11 people?

b One person of weight 83 kg leaves the group.

Find the mean weight of the remaining 10 people.

�6 The mean average salary of 7 people is £26 500.

Gemma joins the group. If she earns £32 100,

what is the mean average salary of all 8 people?

�7 Which kind of average is the most sensible to use to show the

amount of money earned by each person in the UK. Explain why.

TASK 13.2

M�1 The bar chart shows how many goals, Towton United and Hotley Albion,

scored in each of the years shown.

0

10

20

30

40

50

60

Numberofgoals

70

80

2002 2003 2004 2005 2006 Year

Towton UnitedHotley Albion

How many goals did Towton United score in:

a 2002 b 2003 c 2006

d In which year did Hotley Albion score 76 goals?

e In which years did Towton United score the same number of goals?

f How many more goals did Hotley Albion score than Towton United in 2004?

g How many more goals did Towton United score than Hotley Albion in 2006?

h Which team scored more goals during all 5 years and how many

more did they score?

92

�2 In an accident ‘blackspot’, there were 8 accidents in 2001,

10 accidents in 2002, 6 accidents in 2003, 14 accidents in

2004 and 4 accidents in 2005. Copy and complete the pictogram

below:

2002

2003

2004

2005

2001

means 4 accidents

�3 The graph below shows how many males and females work at an

electronics firm called ‘Manucomp.’

019851980 1990 1995 2000 2005

10

20

30

40

50

malefemaleNumber

ofpeople

Year

How many female workers were there in:

a 1985 b 2000 c 2005

d In what year were there the same number of male and female

workers?

e How many more female workers than male workers were there

in the year 2000?

f What was the rise in female workers between 1980 and

2005?

93

E�1 Stem Leaf

1 7 9

2 4 4 5 8 9 9

3 2 6 6

4 3 8 8 8

5 1 4

Key 2j4 = £24

This stem and leaf diagram shows how much money was

raised by some children on a sponsored ‘silence.’

a Write down the median amount

of money.

b What is the range for these amounts

of money?

�2 The weights of 22 people were recorded to the nearest kg.

64 71 63 78 82 49 71 65 74 78 53

58 82 66 65 71 87 65 53 72 68 81

a Show this data on a stem and leaf diagram.

b Write down the range of this data.

�3 The heights of the players in two hockey teams, the Tampton Trojans

and Mallow Town, are shown in the back-to-back stem and leaf diagram.

The Tampton Trojans Mallow Town

15 6

9 3 16 1 8 8

8 5 5 2 1 17 2 4 7 7

4 4 3 18 3

6 19 0 2

Key 2j17 = 172 Key 18j3 = 183

a Find the median and range for Mallow Town.

b Find the median and range for the Tampton Trojans.

c Write a sentence to compare the heights of the players in each

hockey team (use the median and range).

TASK 13.3

M�1 The table below shows how a group of people

get to work each morning.

a Find the total frequency.

b Work out the angle for each person to help

draw a pie chart. (i.e. 360� 4 ‘total frequency’)

c Work out the angle for each type

of transport and draw a pie chart.

type of

transport

frequency

(number

of people)

bus 30

car 10

tube 25

on foot 15

bike 10

94

In Questions�2 and�3 , work out the angle for each item and draw a pie chart.�2 Favourite type of film �3 Favourite colour

film frequency

adventure 6

comedy 18

horror 7

romance 2

cartoon 12

colour frequency

blue 23

green 8

red 28

yellow 41

purple 4

other 16

E�1 300 people were asked what their favourite hot drink is.

The pie chart shows the findings.

How many people chose: others coffee

tea

120°

150°

a coffee b others c tea

�2 This pie chart shows the favourite ‘spirits’ chosen

by 480 people.

How many people chose: others

brandy

vodka

whisky

gin

60°

72°30°

18°

a vodka b gin c brandy

�3 10,000 people were surveyed about which continent they

would prefer to buy their car from.

The pie chart shows this information.

Find the angle on the pie chart for:

others

America

Europe

Asia10%

40%

15%

35%

a Europe b Asia c America

95

�4 The pie charts below show

the favourite sports of

students from Canning

High School and Henton

Park School.football

basketball

hockey

rugby

others

Canning High School

football

basketball

hockey

rugby

others

Henton Park School

Explain why you cannot say that more students like football in

Canning High School than in Henton Park School.

TASK 13.4

M only�1 400 people were asked if they could drive or not. The information is

shown in the two-way table.

drive

not

drive Total

Female 110 170

Male

Total 290 400

a Copy and complete the table.

b How many males could not drive?

�2 When they last recycled something, 600 children were asked if they

recycled paper, bottles or cans. The information is shown in the

two-way table below.

paper bottles cans Total

Boys 73 89

Girls 352

Total 306 131 600

a Copy and complete the two-way table.

b How many girls recycled paper last time they recycled

something?

96

�3 Some people were asked if they would rather watch a film on a dvd,

at the cinema or go to the theatre.

The results are shown below:

M = Male, F = Female, d = dvd, c = cinema, t = theatre

M, c M, c F, c F, d F, c

F, d F, t F, d M, t M, c

M, c F, c M, c F, t F, d

F, d F, d M, t M, d F, c

a Put these results into a two-way table.

b What percentage of the males chose the theatre?

�4 500 students in the Kingsley High School were asked what they planned

to do after Year 11. The results are shown in the two-way table below.

stay in 6th.

form go to college

leave

education Total

Year 10 26

Year 11 120 109 31

Total 206 500

a Copy and complete the two-way table.

b One of these students is picked at random. Write down the

probability that the student is in Year 10.

c One of these students is picked at random. Write down the

probability that the student plans to go to College.

SHAPE 3 15

TASK 15.1

M�1 Find the perimeter of each shape below. All lengths are in cm.

a

85

7

b 9

3

c 7

7

97

�2 Draw 3 different rectangles with a perimeter of 14 cm.

�3 For each shape below you are given the perimeter. Find the missing value x.

All lengths are in cm.

a

9 6

x

perimeter = 23 cm

b

perimeter = 35 cm

14

12

x

c

perimeter = 30 cm

5

5

x

�4 The perimeter of this square is 24 cm.

Find the missing value x.

x

x

x

x

�5 The perimeter of these two rectangles is the same. Find the missing value x.

12

3

x

9

E�1 All lengths are in cm.

a Find the length of a and b.

b Find the perimeter of this shape.

16

13

6

5a

b

98

In Questions�2 to�4 , find the perimeter of each shape. All lengths are in cm.�2

3

12

10

5 �3

2 2

3

665

�4 14

4

7

5

The perimeter of these two shapes is the same. Find the missing value x.�5

21

10

66

77

�624

5

8

x

TASK 15.2

M

Find the area of each shape below. All lengths are in cm.�1 5

4

�2 6

5

�3 11

7

�4 6

10

�54

8

�696

99

�7 Find the value of x.

Area = 48 cm2

8 cm

x

Find the area of each shape in Questions�8 to�13 by splitting them into rectangles

or triangles.�8 5

4 8

3

�9

14

4

6

9

�10

7 7

5

3 3

6

�11 12

10

4

�12

14

10

8

�13

25

20

7

E

Find the area of each shape below. All lengths are in cm.�1 3

17

6

�210 619

�3 8

9

100

�4 The area of this trapezium is 80 cm2.

What is the value of h?3 cm

7 cm

h

�5 The area of the parallelogram

is equal to the area of the

trapezium. Find the

value of x.

x cm

6 cm

8 cm6 cm 12 cm

�6 Find the shaded area.

20 m

24 m40 m

30 m

TASK 15.3

M�1 What is the radius of a circle if the diameter is 46 cm?

�2 What is the diameter of a circle if the radius is 19 mm?

�3 Use a calculator to find the circumference of each circle below (give answers to

1 decimal place).

a

12 cm

b

3 m

c

9 cm

d

17 m

101

�4 Which shape has the larger perimeter – the

triangle or the circle?8 cm

9 cm

5 cm 6 cm

�5 Which circle has the larger perimeter?

4 cm

A

7 cm

B

E

Calculate the perimeter of each shape. All arcs are either semi-circles

or quarter circles. Give answers correct to 1 decimal place.

�116 cm

�231 cm

�35 cm

5 cm

�44 cm

12 cm �5 100 m

32 m

�63 m

6 m

3 m

�7 A circular log of diameter 30 cm is rolled down a hill. It rolls

48 metres. How many complete revolutions did the log make

before it stopped?

�8 Maisy has a bike with wheels of radius 31·5 cm. She cycles 3 km.

How many times do the wheels of her bike go round

completely?

102

TASK 15.4

M

Calculate the area of each circle below, correct to 1 decimal place.

�15 cm�2

9 cm

�312 cm

�432 cm

�5 A circular pond has a radius of 11 m. What is the area of this pond in m2?

�6 Which shape has the larger area – the

triangle or the circle?5 cm

3 cm

4 cm1·5 cm

�7 Find the shaded area. 8 cm

8 cm

E

In Questions�1 to�3 find the area of each shape. All arcs are either

semi-circles or quarter circles and the units are cm. Give answers

correct to 1 decimal place.�124

�25·4

5·4

�3 68

16

103

In Questions�4 to�6 find the shaded area. Lengths are in cm. Give answers

correct to 1 decimal place.�48 33

�514

28 �69

5

5

�7 A circular pond has a radius of 13 m. A path goes all the way round the circumference

of the pond. The path is 1·2 m wide throughout. Find the area of the path.

TASK 15.5

M�1 Copy and complete the table below to find the total surface area of the cuboid.

9 cm

4 cm6 cm

face area (cm2)

front

back

top

bottom

side 1

side 2

Total =�2 Find the volume in cm3 of the cuboid in Question�1 .

�3

6 cm

5 cm13 cm

A

8 cm

4 cm B 10 cm C 14 cm5 cm

5 cm

a Which of these 3 cuboids has the largest surface area?

b What is the difference between the largest surface area and the smallest surface area?

c Which of the cuboids has the smallest volume?

d What is the difference between the largest volume and the smallest volume?

104

E�1 Which is the greater amount? 7·2 m3 or 7 090 000 cm3

Remember:

1 m3 = 1000 litres

1 m3 =

1 000 000 cm3

1 m2 = 10 000 cm2

�2 True or false? 6·3 m2 = 630 cm2

�3 Does 5·84 m3 = 58 400 cm3 or 5 840 000 cm3?

�4 How many litres of water will each tank below

contain when full?

a

9 m

5 m12 m

b

18 m

4·2 m3·6 m

�5 A rectangular tank has a length of 8 m and a width of 6 m.

How high is the tank if it can hold 240 000 litres of water when

full?

�6 Copy and complete

a 4 m3 = cm3 b 2·9 m3 = cm3 c 8 m2 = cm2

d 7·48 m2 = cm2 e 6 000 000 cm3 = m3 f 6 m3 = litres

g 6 000 000 cm2 = m2 h 5·16 m3 = litres i 38 000 cm2 = m2

j 473 000 cm2 = m2 k 12·64 m3 = litres l 0·07 m3 = cm3

TASK 15.6

M

Find the volume of each prism below:Remember:

Volume of a

prism = area of

cross-section ·length

�1

6 cm

9 cm

10 cm

�2

12 m

9 m

4 m6 m

3 m

105

�3

10 cm

7 cm15 m

�4

13 cm

4 cm

3 cm

25 cm

�5

13 cm

15 cm

8 cm

8 cm

30 cm

4 cm

4 cm

�6 The volume of a prism is 296 cm3. If the length of the prism is 8 cm,

what is its cross-sectional area?

E

Find the volume of each cylinder below. Use a calculator and give

each answer to 1 decimal place.�15 cm

20 cm

�2 18 cm

9 cm

�329 cm

2 cm

�4 A pipe of diameter 8 cm

and length 3 m is half full

of water. How many litres

of water are in the pipe?Remember:

1 m3 = 1000 litres

and change

8 cm into metres

106

�5 Find the volume of this prism.

21 cm

8 cm

8 cm

�6 A cylindrical bucket has a diameter of

30 cm and a height of 35 cm.

How many full bucket loads of water

are needed to fill up the tank opposite?

45 cm

85 cm

60 cm

TASK M15.7

M�1 a Explain why these triangles are similar.

b Find x.4 cm

5 cm50°

55°20 cm

55°

50°x

�2 Find y.

6 cm

4 cm130°

10°

28 cm

130°

10°

y�3 Use similar triangles to find x.

10 cm

2 cmx

5 cm

107

�4 Use similar triangles to find y.

8 cm

12 cm

6 cm y

�5 Use similar triangles to find x in each diagram below.

a

4 cm

x

10 cm

15 cm

b

4 cm36 cm

45 cm

x

E�1 a and b are lengths.

H = ab2 Is this a formula for a length, area or volume?

�2 r is a length.

p = 4pr Is this a formula for a length, area or volume?

�3 Each letter below is a length. For each expression write down if it represents

a length, area or volume.

a 3h b x2 c 4xy

d pabc e 3px f pxy

g 6pr h 3x2y i 4rh

j 5r k 4xyz l 7x

m 3pab n 2pa2 o 5y3

�4 a, b and c are lengths.

Which of the formulas below represent a volume?

6a3 pac 7pb pb2c 2ab2

108

DATA 3 16

TASK 16.1

M�1 The table below shows the English test results and heights of 16 students.

Score (%) 82 53 80 76 67 46 67 71 61 83 72 48 73 75 59 45

Height (cm) 175 182 193 160 168 165 183 197 159 163 175 161 164 188 170 193

a Copy and complete this scatter

graph to show the data in the table.

16040 50 60 70 80 90

170

180

190

200

Score

%

Height

b Describe the correlation in this

scatter graph.

�2 Describe the correlation in this scatter graph.

E�1 Write down what X and Y might be to give this

scatter graph.

X

Y

109

�2 The table below shows the heights and neck lengths of 14 people.

height (cm) 177 187 195 162 200 175 192 186 165 200 172 198 181 190

neck length (cm) 6·9 7·5 7·5 5·5 8·5 6·1 6·8 6·8 6 8 5·7 7·7 6·9 7·8

a Copy and complete this scatter graph

to show the data in the table.

160 170 180 190 2004

5

6

7

8

9

height (cm)

necklength (cm)

b Describe the correlation.

c Draw the line of best fit.

d A person is 184 cm tall. Use your line

of best fit to find out the person’s

likely neck length.

e Another person has a neck length of

7·7 cm. How tall is that person likely

to be?

�3 This scattergraph shows information

about cars. Write down what you

think Y might be.

Y

Age

TASK 16.2

M�1 The table below shows the weights of some people.

Weight (kg) 60 61 62 63

Frequency 3 6 5 1

Find a the modal weight

b the median weight

110

�2 The table below shows the number of drinks some children had

during one day.

Number of drinks 1 2 3 4 5

Frequency 7 12 8 23 29

Find a the modal number of drinks

b the median number of drinks

�3 The 2 tables below show the number of GCSE grade Cs obtained

by some students.

Number of C grades 1 2 3 4 5

Frequency 20 38 18 27 24Boys

Number of C grades 1 2 3 4 5

Frequency 26 20 41 39 67Girls

a Find the median number of C grades for the boys.

b Find the median number of C grades for the girls.

c Which group has the higher median number of C grades?

E�1 The table below shows how many times some people ate meat during one week.

Number of times

meat eaten0 to 1 2 to 5 6 to 8 over 8

Frequency 75 51 104 17

Find a the modal interval

b the interval which contains the median

�2 The table opposite shows the neck sizes of a group

of people.

Find a the modal interval

b the interval which contains the median

Neck size (cm) Frequency

12 to 14 36

141

2to 151

281

16 to 161

275

17 to 171

229

over 171

214

111

�3 Some students from nearby schools are asked how often they go

each month to a local skateboard park. The information is shown

in the tables below.

Chetley Park School

Park Visits Frequency

0 to 1 27

2 to 5 21

6 to 9 15

10 or more 8

Wetton School

Park Visits Frequency

0 to 1 19

2 to 5 23

6 to 9 34

10 or more 17

a For each school, find the interval which contains

the median.

b From which school do students generally go to the skateboard park

more often? Explain why you think this.

TASK 16.3

M

Use a calculator if you need to.�1 Some young people were asked how many different mobile phones

they had owned during the last 6 years. The information is shown in

the table below.

Number of phones 0 1 2 3 4

Frequency 7 4 12 14 3

a Find the total number of phones.

b Find the mean average number of phones.

�2 Some people were asked how many

computers they had in total in their

houses.

a Find the total number of computers.

b Find the mean average number of

computers per house (give your

answer to 1 decimal place).

Number of

computers Frequency

0 16

1 26

2 37

3 20

4 5

112

E�1 Some people were asked how many times they ate out in a restaurant

or pub during one month. The information is shown below.

Number of

meals (m)0 < m < 2 2 < m < 5 5 < m < 10 10 < m < 20

Frequency 24 39 16 12

a Estimate the total number of meals.

b Estimate the mean average (give your answer to the nearest whole number).

c Explain why your answer is an estimate.

�2 The number of goals scored by two hockey teams over the last 15 years is

shown in the tables below.

Batton City

Number of goals (g) Frequency

20 < g < 30 2

30 < g < 40 3

40 < g < 50 5

50 < g < 60 4

60 < g < 70 1

Chorley Town

Number of goals (g) Frequency

20 < g < 30 2

30 < g < 40 6

40 < g < 50 4

50 < g < 60 3

60 < g < 70 0

a Which team has scored the higher mean average number of goals?

b Write down the value of the higher mean average (give your answer

to one decimal place).

c What is the difference between the mean average number of goals

scored by each team?

TASK 16.4

M�1 The hourly rates of pay for 5 workers at a baker’s shop are £5·30, £5·30,

£6·80, £5·75 and £7·25.

The hourly rates of pay at a butcher’s shop for 6 workers are £5·65, £6·75, £8·30, £5·90,

£5·90 and £6.

Copy and complete the statements below to compare the pay rates of the 2 shops.

Baker’s shop: median = £____ range = £____

Butcher’s shop: median = £____ range = £____

‘The median for the baker’s shop is (greater/smaller) than the median for thebutcher’s shop. The range for the baker’s shop is (greater/smaller) than the rangefor the butcher’s shop (i.e. the pay rates for the baker’s shop are (more/less) spread out).’

113

�2 The number of ‘fizzy’ drinks drunk each week by some children is shown below:

Class 8C: 2 3 2 5 3 0 1 2 1 3 6 4 3 4

Class 8D: 0 3 1 7 2 0 2 5 6 2 3 1 2

Copy and complete the statements below to compare the number of

‘fizzy’ drinks drunk by these children in class 8C and class 8D.

Class 8C: mode = ____ range = ____

Class 8D: mode = ____ range = ____

‘The mode for class 8C is (greater/smaller) than the mode for class 8D and the

range of class 8C is (greater/smaller) than the range of class 8D (i.e. the number

of ‘fizzy’ drinks drunk in class 8C is (more/less) spread out).’

E�1 Sam and Polly record the number of e-mails they receive each day during January.

The information is shown below:

10 2 3 4 5 6 7012345

Frequency

Number of e-mails

Sam

10 2 3 4 5 6 7012345

Frequency

Number of e-mails

Polly

a Work out the mean and range for Sam.

b Work out the mean and range for Polly.

c Write a sentence to compare the number of e-mails received each day by Sam and Polly.

�2 Some 8 year-olds and some 18 year-olds are asked how many Christmas

presents they had last Christmas.

8 year-olds

0 to 8 6

9 to 16 31

17 to 24 48

25 to 32 10

33 to 40 3

41 to 48 2

18 year-olds

0 to 8 34

9 to 16 26

17 to 24 9

25 to 32 5

33 to 40 1

41 to 48 0

a Estimate the mean average for the 8 year-olds.

b Estimate the mean average for the 18 year-olds.

c Compare the number of Christmas presents received by the

8 year-olds and the 18 year-olds.

114

SHAPE 4 17

TASK 17.1

M

Write down the time shown by each clock below:�1 12 1

2

3

4567

8

9

1011 �2 12 1

2

3

4567

8

9

1011 �3 12 1

2

3

4567

8

9

1011

�4 12 1

2

3

4567

8

9

1011 �5 12 1

2

3

4567

8

9

1011 �6 12 1

2

3

4567

8

9

1011

�7 Write down the measurement indicated by each arrow.

10 20 30 40 50 60

a b c d e

f Write down the difference between d and b.

g Write down the difference between e and a.

�8 Write down the measurement shown by each arrow below.

500

600

700

800

ab

c

60

50

40 3020

10

0litres

400grams

300200

100

0

d e

115

E�1 Write down the measurement indicated by each arrow.

1 2 3 4 5 6

a b c d e

f Write down the difference between d and a.

g Write down the difference between e and b.

�2 Write down the measurement shown by each arrow below.

a

0·5

1·5

2·5

3

1 2

0

kg

b

0·1

0·20·3

0·4

0·5

0·60kg

c

3

4

12

0litres

d

1000

800600

400

200

01200ml

�3 Write down the measurement shown by each arrow below.

9

8

7

6

kg

a

b

17

16

15

14litres

c

d0·04

0·03

0·02

0·01kg

e

f

116

TASK 17.2

M�1 Write each length in cm.Remember:

10 mm = 1 cm

100 cm = 1 m

1000 m = 1 km

1000 g = 1 kg

1000 kg = 1 tonne

1000 ml = 1 litre

1 ml = 1 cm3

a 3 m b 1·2 m c 5·8 m d 3·64 m e 0·7 m�2 Write each mass in grams.

a 4 kg b 6·5 kg c 3·2 kg d 4·718 kg e 0·9 kg�3 Which metric unit would you use to measure:

a the length of a car b the mass of a car c the width of a pin�4 Sam says that his dad weighs about 80 grams. Is this likely to be

a good estimate?�5 Write each length in metres.

a 600 cm b 450 cm c 5 km d 5·3 km e 7·186 km�6 Write each quantity in ml.

a 8 litres b 9·5 litres c 4·6 litres d 4·315 litres e 60 cm3

�7 Venkata has a 1 litre bottle of lemonade. If 560 ml of lemonade is

used, how much is left in the bottle?�8 Toby is running in a 3 km race. He has covered 900 metres. How much

further to the end of the race?

E�1 Barry buys a 2·5 kg bag of potatoes. If he uses up 820 g of

potatoes, what weight is left in the bag?

�2 Beth walks 3·8 km and Simone walks 937 m. How much further

has Beth walked than Simone?

�3 Copy and complete the following:

a 2·6 m = cm b 3·82 m = cm c 470 cm = m

d 90 mm = cm e 4 mm = cm f 1500 m = km

g 3·5 kg = g h 600 g = kg i 0·28 kg = g

j 1·9 tonnes = kg k 620 ml = litres l 1937 litres = ml

m 8·2 litres = ml n 3·26 litres = ml o 43 g = kg

�4 A shop uses 40 g of cheese in one sandwich. How many sandwiches

will the shop make if it has 3·2 kg of cheese?

�5 Write the following amounts in order of size, starting with the smallest.

a 8 cm, 0·81 m, 7·4 cm, 83 mm

b 780 g, 0·7 kg, 738 g, 0·79 kg

c 5 km, 57 m, 509 m, 0·6 km, 4·7 km

d 274 ml, 0·28 l, 0·279 l, 275 ml, 2·14 l

117

TASK 17.3

M�1 For each statement below, write true or false:

a 8:30 p.m. = 20:30 b 4:30 a.m. = 16:30

c 2:15 a.m. = 02:15 d 3:42 a.m. = 03:42

e 10:50 p.m. = 10:50 f 5:17 p.m. = 17:17

�2 Sunil watches a 2 hour 15 minute film which starts at 7:50 p.m.

At what time does the film end?

�3 Patsy flies to Rome and arrives at 13:35. If the flight lasted for 2 hours

45 minutes, when did the flight begin?

�4 Gabby borrows some money and has to pay it back within 5 years.

How many months does she have to pay back the money?

�5 Gareth wakes up at the time shown on the clock.

He has to be at work by 9 a.m. How long has he

got before he must be at work?

�6 Andre needs to be at Waterloo station by 5:30 p.m. A train leaves his

home town at 15:48 and takes 1 hour 40 minutes to get to Waterloo

station. Will he arrive at Waterloo station in time?

�7 Copy and complete this bus timetable. Each bus takes the same time

between stops.

Bus 1 Bus 2 Bus 3 Bus 4 Bus 5

Bus Station 07:50 08:35 08:55 09:45 10:25

Cinema 07:59

Town Hall 08:10

Cherry Hill 08:22 09:27

Train Station 08:35 10:30

E�1 Write each length in inches.Remember:

12 inches = 1 foot

3 feet = 1 yard

1760 yards = 1 mile

8 pints = 1 gallon

16 ounces = 1 pound

14 pounds = 1 stone

2240 pounds = 1 ton

a 5 feet b 8 feet c 5 feet 4 inches d 4 feet 9 inches

�2 Write each volume in pints.

a 3 gallons b 5 gallons c 31

2gallons d 23

4gallons

�3 Which imperial unit would you use to measure:

a the mass of a man

b the length of a book

c the height of a house

118

�4 Mary is 4 feet 10 inches tall when she is 11 years old. Over the

next 5 years she grows 7 inches. How tall is she now?

�5 Jade runs 1285 yards. How much further must she run to complete

1 mile?

�6 Copy and complete the following:

a 2·5 gallons = pints b 3 stone 2 pounds = pounds

c 5 stone 9 pounds = pounds d 3 miles = yards

e 36 pints = gallons f 98 pounds = stone

g 5 tons = pounds h 7 stone 12 pounds = pounds

i 11

2tons = pounds j 5 feet 10 inches = inches

TASK 17.4

M�1 Copy and complete:Remember:

1 inch � 2·5 cm

1 foot � 30 cm

1 yard � 90 cm

1 mile � 1·6 km

1 ounce � 30 g

1 kg � 2·2 pounds

1 litre � 1·8 pints

1 gallon � 4·5 litres

a 10 gallons � litres b 20 kg � pounds

c 4 gallons � litres d 6 inches � cm

e 10 miles � km f 21

2feet � cm

g 18 ounces � g h 27 litres � gallons

i 17·5 cm � inches j 31

2yards � cm

�2 Harry cycles 20 miles. Louise cycles 30 km. Who cycles further?

�3 Tom needs 6·5 pounds of flour. If he buys a 2 kg bag of flour and

a 1 kg bag of flour, will he have enough flour?

�4A

If each container is

filled up with water,

which container will

hold the most?

B

�5 Which amount is the smaller?

a 3 gallons or 14 litres? b 8 miles or 12 km?

c 5 km or 3 miles? d 5 kg or 10 pounds?

e 8 yards or 700 cm? f 35 litres or 8 gallons?

g 9 inches or 23 cm? h 4 feet or 1 m?

119

E�1 The length of a book is 23·4 cm, measured to the nearest 0·1 cm.

23·3

Lower bound Upper bound

23·4 23·5

Write down

a the lower bound b the upper bound

�2 The width of a room is 3·8 m, measured to the nearest 0·1 m.

Write down

a the lower bound b the upper bound

�3 A woman weighs 63 kg, correct to the nearest kg. What is her least

possible weight?

�4 Copy and complete the table.

A length l is 47·2 cm, to the nearest 0·1 cm, so < l < 47·25

A mass m is 83 kg, to the nearest kg, so < m <

A volume V is 7·3 m3, to the nearest 0·1 m3, so < V <

A radius r is 6·87 cm, to the nearest 0·01 cm, so < r <

An area A is 470 m2, to the nearest 10 m2, so < A <

�5 The base and height of a triangle are

measured to the nearest 0·1 cm.

3·4 cm

4·8 cm

a Write down the upper bound for the

base 3·4 cm.

b Write down the lower bound for the

height 4·8 cm.

c The area of the triangle is 1

2(base · height).

Use a calculator to find the greatest

possible value of the area of the

triangle.

�6 The length, width and height of the cuboid

are measured to the nearest cm.

volume = length · width · height

Use a calculator to find the lowest possiblevalue of the volume of the cuboid.

7 cm

9 cm

4 cm

120

TASK 17.5

M

Use DS T

to help you work out the Questions below:

�1 Find the speed for each distance and time shown below.

a distance = 60 miles, time = 3 hours

b distance = 325 km, time = 5 hours

�2 Find the distance for each speed and time shown below.

a speed = 45 mph, time = 2 hours

b speed = 58 mph, time = 1

2hour

�3 Find the time taken for each distance and speed shown below.

a distance = 280 km, speed = 70 km/hr

b distance = 50 km, speed = 20 km/hr

�4 Copy and complete this table.

Distance (km) Time (hours) Speed (km/hr)

324 9

4 51

1·5 60

150 25

245 35

40 0·5

�5 Jack cycles 3 km in 15 minutes. What was his average speed in km/hr?

�6 Brenda drives from Nottingham to Leeds at an average speed of

84 km/hr. The journey takes 1 hour 30 minutes. How far is it from

Nottingham to Leeds?

�7 A train travels 47 km in 20 minutes. What is the speed of the train in

km/hr?

�8 Ellen drives 24 km from her home to work. She travels at an average

speed of 32 km/hr. If she leaves home at 8·05 a.m., when will she

arrive at work?

E

Use MD V

to help you work out the Questions below:

�1 A solid weighs 450 g and has a volume of 50 cm3. Find the density

of this solid.

121

�2 A liquid has a density of 2 g/cm3. How much does the liquid weigh

if its volume is 240 cm3?

�3 A metal bar has a density of 12 g/cm3 and a mass of 360 g.

Find the volume of the metal bar.

�4 Copy and complete this table.

Density (g/cm3) Mass (g) Volume (cm3)

7 90

240 60

8 152

42 0·5

13 585

1·5 140

�5 Gold has a density of 19·3 g/cm3. A gold ring has a volume of 1·1 cm3.

Find the mass of the gold ring.

�6 A brass handle has a volume of 17 cm3 and a mass of 139·4 g.

Find the density of the brass.

�7 Which has a greater volume 2102·6 g of lead with density

11·4 g/cm3 or 78·85 g of steel with density 8·3 g/cm3? Write down by

how much.

�8 The density of this metal bar is

7·4 g/cm3.

Find the mass of this metal bar.

Give your answer in kg.

(Note the length is given in metres)

8 cm

5 cm 1·2 m

�9 A curtain material costs £38 per metre. How much will 4·5 m

cost?

�10 Each year a farmer makes a profit of

90p per m2 in this triangular

field. How much profit does

he make in total?

Give your answer

in pounds.

130 m

200 m

122

ALGEBRA 4 18

TASK 18.1

M

Copy and complete each statement below:

�1 If a = b + 4 then a 4 = b �2 If y = x + 6 then y 6 = x�3 If x = 4y then x = y �4 If a = b

8then a = b

�5 a = b 2 10 Make b the subject of the formula.

�6 n = 5m Make m the subject of the formula.

�7 Make n the subject of each formula given below:

a m = n + 9 b m = 4n c m = n

3d m = n 210

�8 Write down the pairs of

equations which belong to

each other.

y = 8x y = x8

8y = x = xy8

�9 Write down which working out below is correct.

a m = 4n + 8

m + 8 = 4nm + 8

4= n

b y = 2x 2 6

y + 6 = 2xy + 6

2= x

�10 Make n the subject of each formula given below:

a m = 3n + 5 b m = 7n 2 1 c m = n

42 6

E�1 Which statements below are true or false?

a m = np + v so m 2 v = np

b y = mx + c so y + c = mx

c p = qs 2 r so p + r = qs

d mx = y + c so x =y + c

m�2 Make n the subject of each formula given below:

a m = cn 2 f b x = gn + h c an 2 2m = y

123

�3 Copy and fill each box below:

a a(x + b) = y

ax + = y

ax + 2 = y 2

ax = y 2

x =y 2

a

b p(t 2 2) = 3q

pt 2 = 3q

pt 2 + = 3q +

pt = 3q +

t =3q +

�4 Make n the subject of each formula given below:

a m(n + p) = v b x(n + f ) = y c h(n 2 3) = x

�5 an 2 b

3= c Make n the subject of the formula.

�6 mx + c

a= b Make x the subject of the formula.

�7 y = 3(b + c)

mMake b the subject of the formula.

TASK 18.2

M�1 Copy and fill each box below with < or >.

a 15 19 b 2·4 1·4 c 302 299 d 23 24

�2 Answer true or false:

a 3·09 > 3·1 b 28 < 24 c 31

4> 3·5 d 6·81 > 6·59

�3 If n < 4·5, which of the values for n below would be allowed?

4·2 41

44·75 4·06 41

24·914

�43

shows x > 3

2shows x , 2

Write down the inequalities shown below:

a

6b

−3c

−1

d

62e

3−2f

0−4

�5 Draw a number line to show the following inequalities.

a x > 1 b x < 26 c 4 < x < 9

d 22 < x < 0 e 23 < x < 2 f 25 < x < 21

124

E

Solve the inequalities below:�1 x + 6 > 12 �2 x + 3 < 22 �3 x 2 4 < 7�4 x 2 6 < 0 �5 4x > 12 �6 x

2> 9�7 3x + 2 > 17 �8 4x 2 8 < 12 �9 2(x + 3) < 18�10 6(x 2 2) > 24 �11 6x 2 4 > 3x + 17 �12 x

42 3 < 3

�13 Write down the largest integer x for which 2x < 7.

�14 Write down the largest integer x for which 5x < 12.

�15 Write down all the integer values (whole numbers) of x which

satisfy each inequality below.

a 4 < x < 7 b 0 < x < 5 c 22 < x < 0

d 23 < x < 3 e 24 < x < 21 f 26 < x < 1

TASK 18.3

M�1 Work out and write each answer as a number in index form.Remember:

am · an = am+n

am 4 an = am2n

a 53 · 54 b 64 4 62 c 38 4 33

d 94 · 92 e 27 · 2 f 49 4 4

g 23 · 24 · 22 h 53 · 5 · 53 i 56 · 52 4 54

�2 Copy and complete

a 26 · 2 = b 34 · = 39 c · 63 = 67

d 57 4 = 52 e 812 4 = 811 f 4 46 = 42

�3 Answer true or false for each statement below.

a 24 · 2 = 24 b 42 · 44 = 48 c 78 4 72 = 76

�4 Work out and write each answer as a number in index form.

a 36 · 34

37b 53 · 52 · 52

55c 97

93 · 9

E�1 Work out and write each answer as a number in index form.Remember:

(am)n = amn

a0 = 1

a (42)3 b (23)3 c (74)2

d (52)4 · 53 e (62) · (62)2 f(32)5

36

g 43 · (43)4 h(22)6

(23)3i

74 · (73)2

75

125

�2 What is the value of 80?

�3 Simplify the expressions below.

a x4 · x3 b y7 · y2 c a6 4 a2

d m7

m3e (x2)4 f x0

g (y5)3 h (a0)3 i (x3)2 4 x2

�4 Answer true or false for each statement below.

a (x4)5 = x9 b y4 · y2 = y8 c x3 · x = x3

d n6

n= n5 e

(x3)3

(x2)3= x3 f

(a2)4

a= a6

�5 Which rectangle has

the larger area?

43

(42)4

A46

44

B

�6 Simplify the expressions below.

a n4 · n2

n5b

(x2)2 · x5

x6c

a · (a3)3

(a3)2

d(x2)6 · x2

(x7)2e m9

m2 · m5f n10

(n3)2 · n2

g(x3)4 · (x2)5

(x3)6h m19

(m2)4 · (m5)2i

(x3)3 · (x2)5

(x6)2 · (x2)2

�7 Answer true or false for each statement below.

a 3x · 3x = 9x2 b 5x2 · 4x3 = 20x6

c (3a2)2 = 9a4 d 15x7

3x4= 5x3

TASK 18.4

M�1 Write the numbers below in standard form.Remember:

a standard form

number will have

the form A · 10n

where 1 < A < 10

a 3000 b 70 000 c 340 d 89 000

e 486 000 f 598 g 9 million h 76 million

�2 Remember that 570 = 5·7 · 102 but 0·057 = 5·7 · 1022. Write the

number below in standard form.

a 0·004 b 0·0007 c 0·9 d 0·0018

e 0·528 f 0·000019 g 0·0034 h 0·00000817

126

�3 Write each number below as an ordinary number.

a 6 · 104 b 3 · 102 c 3 · 1022 d 5·6 · 104

e 2·4 · 105 f 8·6 · 1023 g 4·16 · 103 h 7·68 · 1021

�4 3700 = 37 · 102. Explain why this number is not written in standard form.

�5 28 000 = 28 · 103. This number is not written in standard form. Write

it correctly in standard form.

�6 Write the numbers below in standard form.

a 0·0007 b 53 000 c 0·096 d 0·487

e 49 000 000 f 576 000 g 0·00074 h 82·4

i 0·1 j 0·000000864 k 6 180 000 l 42 000 000

E�1 Use a calculator to work out the following and write each answer in standard form.

a (7 · 108) · (4 · 109) b (6·2 · 105) · (3 · 1034)

c (4 · 1028) · (6 · 1037) d (3·6 · 1014) 4 (3 · 10214)

e (7·6 · 10229) 4 (2 · 10211) f (5·2 · 1037) + (6·1 · 1036)

�2 The population of the UK is (5·97 · 107) people. The population of

the USA is (2·41 · 108) people. What is the combined population

of UK and USA? (give your answer in standard form)

�3 The mass of an atom is 3·74 · 10226 grams. What is the total mass of

2 million atoms?

�4 Work out the following, leaving each answer in standard form correct

to 3 significant figures.

a(5·6 · 1021) · (2·7 · 1028)

5 · 1013b

(7·4 · 10213) · (3·94 · 10226)

4·2 · 1018

c(3·8 · 1023) 2 (9·7 · 1022)

1·8 · 10217d

(4·89 · 1016)2

2·14 · 109

e(4·83 · 1014) + (3·16 · 1015)

2·82 · 10212f 5·28 · 1031

(4·9 · 10210) + (2·7 · 1029)

�5 Do not use a calculator.

Find the area of this rectangle,

leaving your answer in standard form.(2 × 104) cm

(4 × 105) cm

�6 Do not use a calculator. Work out the following, leaving each answer in standard form.

a (2 · 108) · (2·5 · 107) b (1·5 · 106) · (4 · 103)

c (3·5 · 109) · (2 · 1024) d (1·7 · 10218) · (4 · 1028)

e (4 · 1012) · (3 · 107) f (9 · 1017) · (4 · 1028)

g (8 · 1021) 4 (4 · 106) h (7 · 1019) 4 (2 · 107)

127

i 9 · 1032

4·5 · 1025j (4 · 105)2

k (8·7 · 1012) 4 (3 · 10216) l 3 · 1048

6 · 1013

�7 Do not use a calculator. Calli has £(4 · 105) and Carl has £(3 · 104).

They put their money together. Write down the total amount of

money they have, giving your answer in standard form.

�8 In a TV popstar show final, the number of votes for each contestant is shown below:

Gary Tallow (9·6 · 105) votes

Nina X (1·3 · 106) votes

Rosa Williams (1·85 · 106) votes

How many people voted in total? Do not use a calculator and give

your answer in standard form.

SHAPE 5 19

TASK 19.1

M�1 Measure these lines to the nearest tenth of a centimeter.

a b

c d

e

f

�2 Which shape below has the larger perimeter and by how much?

a b

128

�3 Which shape below has the smaller perimeter and by how much?

a b

E

Using a protractor, measure the following angles.

�1 �2 �3

�4 �5 �6

�7 �8 �9

�10 Use a protractor to draw the following angles. Label each angle

acute, obtuse or reflex.

a 30� b 75� c 49� d 24�e 135� f 113� g 157� h 18�

129

TASK 19.2

M�1 Use a ruler and protractor to draw:

a

50°7 cm

4 cm

b

8 cm

7 cm

35°

�2 a Draw accurately the triangle.

b Measure the length of the

side marked x. 6 cm

7 cm

x

60°

�3 a Use a ruler and protractor to draw the triangle.

b Measure and write down angle a.

7 cm65°35°

a

In Questions�4 to�6 , construct the triangles and measure the lengths of

the sides marked x.

�4

6 cm

x

45° 70°

�5

5 cm

x

125°25°

�6 6 cm

8 cm

75°

x

130

E

In Questions�1 to�3 , use a ruler and compasses only to draw each

triangle. Use a protractor to measure each angle x.

�14 cm 6 cm

7 cm

x

�2 4·5 cm

6·5 cm5 cm

x

�37·5 cm

7·5 cm

6 cm

x

�4 Draw accurately an isosceles triangle with two sides equal to 5·5 cm

and one side equal to 7 cm. Two of the angles should be the same.

Measure one of these angles.

�5 Draw a triangle ABC, where AB = 5·2 cm, BC = 7·1 cm and

AC = 6·3 cm. Measure —ABC.

�6 Draw accurately the diagrams below:

a

8 cm5 cm

5·5 cm

6 cm

x

y

55°

b

5 cm5 cm

6·5 cm

6·5 cm 6·5 cm

x

y

Measure angle x and side y. Measure angle x and angle y.

TASK 19.3

M�1 Draw —ABC = 70�.

Construct the bisector of the angle.

Use a protractor to check that

each half of the angle now

measures 35�.

AB

C

131

�2 Draw any angle and construct the bisector of this angle.

�3 Draw a horizontal line AB of length

7 cm. Construct the perpendicular

bisector of AB. Check that each half

of the line measures 3·5 cm exactly.

A B

�4 Draw any vertical line. Construct the perpendicular

bisector of the line.

�5 a Draw PQ and QR at right angles

to each other as shown.P

Q R8 cm

6 cm

b Construct the perpendicular

bisector of QR.

c Construct the perpendicular

bisector of PQ.

d The two perpendicular bisectors

meet at a point (label this as S).

Measure QS.

�6 a Draw —ABC = 108� by using

a protractor.

b Construct the bisector of this angle.

A

B C108°

c Construct the bisector of one of the

new angles.

d Check with a protractor that you have

now drawn an angle of 27�.

E�1 Construct an equilateral triangle with each side equal to 7 cm.

�2 Construct an angle of 60�.

�3 a Draw a line 8 cm long and mark the point A as shown.

A 3 cm5 cm

b Construct an angle of 90� at A.

132

�4 a Draw a line 10 cm long and mark the point B on the line

as shown.

B 6 cm4 cm

b Construct an angle of 45� at B.

�5 Construct a right-angled triangle ABC, where —ABC = 90�,

BC = 6 cm and —ACB = 60�. Measure the length of AB.

�6 Construct this triangle with

ruler and compasses only.

Measure x. x

8 cm45° 60°

TASK 19.4

M

Draw an accurate scale drawing of each shape below using the scale

shown.

�1

Scale: 1 cm for every 3 m

9 m

6 m

�2

Scale: 1 cm for every 2 m

4 m

4 m

8 m 4 m

4 m2 m

4 m2 m

�3 Make a scale drawing of the front

of this house using a scale of 1 cm

for every 2 m.5 m 2 m2 m

2 m

6 m

133

�4

Lawn

Flower bed

Vegetablepatch

PatioPond

This is a plan of Rosemary’s garden. It has been drawn to a scale

of 1 cm for every 3 m.

a What is the length and width of the lawn? b How wide is the patio?

c What is the diameter of the pond? d What is the area of the vegetable patch?

�5 a How many km is Henton from Catford? Henton

Rigby

Catford

Scale: 1 cm for every 10 km.

b How far is Catford from Rigby?

c How far is Henton from Rigby?

E�1 The model of a statue is made using a scale of 1 : 40. If the statue

is 3·2 m tall, how tall is the model (give your answer in cm)?

�2 A park is 5 cm long on a map whose scale is 1 : 40 000. Find the

actual length (in km) of the park.

134

�3 Copy and complete the table below.

Map length Scale Real length

7 cm 1 : 60 m

5 cm 1 : 2000 m

8 cm 1 : 50 000 km

cm 1 : 100 000 3 km

cm 1 : 4000 320 m

cm 1 : 5 000 000 125 km

�4 The distance between two towns is 25 km. How far apart will they

be on a map of scale 1 : 500 000?

�5 A plan of a house is made using a scale of 1 : 30. The width of the

house on the plan is 40 cm. What is the real width of the house?

(give your answer in metres)

�6 Measure then write down the actual distances (in km)

between:

a Hatton and BowtonHatton

Bowton

Tatley

Scale is 1 : 200 000

b Hatton and Tatley

c Bowton and Tatley

TASK 19.5

M

You will need a ruler and a pair of compasses.�1 Draw the locus of all points which are less than or equal to 3 cm from

a point A.

�2 Draw the locus of all points which are exactly 4 cm from a

point B.

�3 Draw the locus of all points which

are exactly 4 cm from the line PQ. 5 cmP Q

135

�4 A triangular garden has a tree at the corner B. The whole garden

is made into a lawn except for anywhere less than or equal to 6 m

from the tree. Using a scale of 1 cm for 3 m, draw the garden and

shade in the lawn.

9 m

18 m

A

B

C

�5 A square garden has a fence around its perimeter.

A dog inside the garden is attached by a rope to a peg

P as shown. The rope is 30 m long. Using a scale of

1 cm for 10 m, copy the diagram then shade the area

that the dog can roam in.

50 m

40 m

10 mP

�6 Draw the square opposite.

Draw the locus of all the points outside the square

which are 3 cm from the edge of the square.

4 cm

4 cm

E

You will need a ruler and a pair of compasses.�1 Construct the locus of points which are the same

distance from the lines AB and BC

(the bisector of angle B).

A

B C

136

�2 A soldier walks across a courtyard from B so that

he is always the same distance from AB and BC.

Using a scale of 1 cm for 20 m, draw the

courtyard and construct the path taken

by the soldier.

A 100 m

60 m

B

CD

�3 Construct the locus of points

which are equidistant (the same

distance) from M and N.7 cmM N

�4 Draw this square.

Show the locus of points inside the

square which are nearer to Q than to S.

5 cm

P

RS

Q

5 cm

�5 Draw A and B 7 cm apart.

A B

A radar at A has a range of 150 km and a radar at B has a

range of 90 km.

Using a scale of 1 cm for every 30 km, show the area which

can be covered by both radars at the same time.

�6 Draw one copy of triangle ABC

and show on it:

a the perpendicular bisector of QR.

b the bisector of —PRQ.

c the locus of points nearer to PR

than to QR and nearer to R

than to Q.

7 cm

5 cm

Q R

P

137

SHAPE 6 20

TASK 20.1

M�1 Draw an accurate net for this cuboid.

3 cm

6 cm4 cm

�2 This net will fold to make a cube. Copy the net and put a cross X in the

square which will be opposite the � when the cube is made.

�3 This net makes a cuboid. What is the

volume of the cuboid?

2

22

2

22 2

2

22

3

3

3

3

Remember:

volume of a

cuboid = length ·width · height

�4 The two nets below will fold to make cuboids.

Each small square is 1 cm long.

Which cuboid has the greater volume and by how much?

AB

138

E�1 This is a tetrahedron (a triangular pyramid)

Which of these nets will make a tetrahedron?

A B

C

�2 Sketch a net for this triangular prism.

4 cm

2 cm

2 cm

�3 Sketch a net for this solid (called an octahedron).

139

�4 a Draw a circle with radius 4 cm.A

b Keep the compasses set at 4 cm.

Place the compass point on the

circumference of the circle and

draw an arc across the

circumference as shown (A).

c Place the compass point on A and draw an arc

across the circumference. Repeat the

process right around the circumference

as shown.

A

d Join the points as shown to make

a hexagon.

e Use compasses and a ruler to

complete this net for a

hexagonal-based pyramid.5

5

555

55

5

55 5

5

140

TASK 20.2

M

You will need isometric dot paper.�1 Make a copy of each object below. For each drawing state the number

of ‘multilink’ cubes needed to make the object.

a b

�2 Draw a cuboid with a volume of 12 cm3.

�3 How many more cubes are needed

to make this shape into

a cuboid?

�4 a Draw a cuboid with length 8 cm, width 3 cm and height 1 cm.

b Draw a different cuboid with the same volume.

�5 Draw this object from a different view.

E�1 Draw and label the plan and a side elevation for:

a a cuboid

4 cm4 cm

2 cm

b a cone

4 cm

3 cm

141

�2 You are given the plan and two elevations of an

object. Draw each object (on isometric paper if you

wish to).

a frontelevation

sideelevation

plan view

b frontelevation

sideelevation

plan view

c

frontelevation

plan view

sideelevation

d

frontelevation

plan view

sideelevation

�3 Draw a front elevation, plan view and side elevation of each

solid below:

a

frontelevation

sideelevation

b

2 cm

2 cm3 cm

142

TASK 20.3

M�1 4 rabbits escape from their run and

race off in the directions shown.

On what bearing does each rabbit race?

35°70°

20°D

C

B

A

North

40°

Remember:

a bearing is

measured

clockwise from

the North

�2 The point at the centre is called M.

Find the bearing of:

60°

60°

60° 60°

60°

60°

R

North

Q

PT

S

a P from M

b S from M

c R from M

d T from M

e Q from M

�3 Write down the bearing of:

North

Rigby

Barnworth

Hoston

40°

75°

65°

220°

115°

35°210°

290°

30°

North

Northa Barnwoth from Hoston

b Rigby from Hoston

c Rigby from Barnworth

d Hoston from Barnworth

e Hoston from Rigby

143

E�1 Use a protractor to measure the bearing of: North

North

Harwich

Melton

a Harwich from Melton

b Melton from Harwich

�2 Use a protractor to

measure the bearing of:

Baghill

Saxley

Elton

Northa Elton from Saxley

b Elton from Baghill

c Saxley from Baghill

d Baghill from Elton

e Saxley from Elton

f Baghill from Saxley

�3 2 hikers walk 5 km due south and then 7 km on a bearing of 050�.

a Use a scale of 1 cm for every 1 km to show their journey.

b Find the distance of the hikers from their starting point.

�4 A submarine travels 40 km due north and then 65 km on a bearing

of 300�.

a Use a scale of 1 cm for every 10 km to show the submarine’s journey.

b Find the distance of the submarine from its starting point.

144

TASK 20.4

M

You will need a calculator. Give your answers correct to 2 decimal places

where necessary. The units are cm. Remember:

a

b

c

Pythagoras says

a2 + b2 = c2

�1 Copy the statements below and fill the empty boxes.

a x2 = 2 + 2

x2 = 25 +

x2 =

x =ffiffiffiffiffiffiffiffiq

x = 5

6x

b x2 + 2 = 132

x2 + = 169

x2 = 169 2

x2 =

x =ffiffiffiffiffiffiffiffiq

x =

1312

x

�2 Find the length QR.

QR is the hypotenuse.�3 Find the length BC.

BC is one of the shorter sides.

Q

P R7

6

B

A

C

149

�4 Find the length x.

Be careful! Check whether x is the hypotenuse or one of the shorter sides.

a

x

4

2

b

x

5

9

c x

419

d x

43

e

x

917

f

x

6

10

145

E�1 A ladder of length 8 m reaches 6 m up a vertical wall. How far is the

foot of the ladder from the wall?

�2 A rectangular TV screen is 21 inches long and 11 inches wide.

What is the length of the diagonal of the TV screen?

�3 Calculate the perimeter of this triangle.

20 m12 m

�4 A plane flies 100 km due south and then a further 150 km

due east. How far is the plane from its starting point?

�5 A knight on a chessboard moves 2 cm to the right then 4 cm

forwards. If the knight moved directly from its old position to

its new position, how far would it move?

4 cm

2 cm

�6 Calculate the area of this triangle. �7 Find x.

15 cm

39 cm

x

3 m 8 m

19 m

146

�8 Find the height of each isosceles triangle below:

a

h9 cm 9 cm

3 cm3 cm

b

8 cm

12 cm12 cm

TASK 20.5

M

You may use a calculator.�1 a Find the co-ordinates of the midpoint of line PQ.

b Calculate the length PQ.

00123456

1 2 3 4 5 6

P

Q

y

x

�2 a Calculate the length of the line joining (1, 3) to (5, 6).

b Write down the co-ordinates of the midpoint of the line joining (1, 3) to (5, 6).

�3 Copy the grid.

Plot each set of co-ordinates below

in the order given to form two sides

of a rectangle.

Complete the rectangle and write

down the co-ordinates of the

missing vertex (corner).0

y

x1 2 3 4 5−1−1

−2

−3

−4

−5

−2−3−4−5

1

2

3

4

5

a (2, 4), (2, 21), (4, 21), ( , )

b (1, 1), (1, 3), (24, 3), ( , )

c (21, 21), (25, 21), (25, 24), ( , )

147

�4 a Draw an x-axis from 22 to 6 and y-axis from 23 to 3.

b ABCD is a parallelogram. A is (1, 22), B is (21, 22) and C is

(3, 2). Draw the parallelogram.

c Write down the co-ordinates of D.

d Write down the co-ordinates of the midpoint of diagonal AC.

e Calculate the length of the diagonal AC.

E�1 A has co-ordinates (0, 4, 5).

Write down the co-ordinates of

B, C, D, E, F and G.

E

0

G

D

F

CB

y

x

z

A

4

5

9

�2 Each side of this cube is 2 units long.

Write down the co-ordinates of the vertices (corners)

O, P, Q, R, S, T, U and V.

O

QR

SV

UT

P

y

x

z

�3 OABCD is a square-based pyramid.

D is directly above the centre of the square base.

The pyramid has a height of 10 units.

Write down the co-ordinates of vertex D.

O

B

A

D

C8

8

y

x

z

148

�4 a Write down the co-ordinates of

the vertices P, Q, R, S, T, U, V

and W.

b Write down the co-ordinates of

the midpoint of edge VR.

c Write down the co-ordinates of

the midpoint of edge PS.

d Calculate the length PR.

O

V

R

W

S

P Q

UT

7

5

6

−3

y

x

z

149